A survey taken by 150 people revealed that 65 like apple juice while 85 dislike it. One person is randomly chosen from this group. What is the chance that the chosen person dislikes apple juice? Write your answer as a ratio in simplest form.
A- 17/30
B- 65/150
C- 13/30
D- 13/17
The probability of choosing someone who dislikes apple juice is equal to the number of people who dislike it divided by the total number of people:
85/(65+85) = 85/150 = 17/30
Therefore, the answer is A, 17/30.
The number cube is rolled a total of 30 times, and it lands on 3 ten times.
The experimental probability of landing on a 3 is the number of times a 3 was rolled divided by the total number of rolls:
experimental probability of rolling a 3 = number of 3s rolled / total number of rolls
experimental probability of rolling a 3 = 10 / 30
experimental probability of rolling a 3 = 1/3
Therefore, the experimental probability of landing on a 3 is 1/3.
The theoretical probability of getting three heads is:
(1/2) x (1/2) x (1/2) = 1/8
The experimental probability of getting three heads is:
40/100 = 2/5
The difference between the experimental probability and theoretical probability is:
2/5 - 1/8
To subtract these fractions with different denominators, we need to find a common denominator:
(2/5) x (8/8) - (1/8) x (5/5)
= 16/40 - 5/40
= 11/40
Therefore, the difference between the experimental probability of getting three heads and its theoretical probability is 11/40.
A six-sided number cube is rolled 30 times and lands on 3 ten times and on 5 eight times. Calculate the experimental probability of landing on a 3. Write your answer in the simplest form of a fraction.
The experiment involved tossing three coins simultaneously. The experiment was carried out 100 times, and it was noted that three heads occurred 40 times. What is the difference between the experimental probability of getting three heads and its theoretical probability? Write the answer in the simplest form of fraction.
Let X be the random variable representing the number on the card chosen. Then, the probability model for this experiment can be written as:
P(X=2) = 1/4
P(X=4) = 1/4
P(X=6) = 1/4
P(X=10) = 1/4
This is because there are 4 possible outcomes (the 4 number cards) and each outcome has an equal chance of occurring (since they are all equally likely to be chosen).
If the probability of selecting a supermarket shopper who prefers plastic bags is 50%, then we can expect that about half of the shoppers will prefer plastic bags.
To find out how many shoppers out of 150 we can expect to prefer plastic bags, we can multiply the total number of shoppers by the probability of selecting a shopper who prefers plastic bags:
Expected number of shoppers who prefer plastic bags = (probability of selecting a shopper who prefers plastic bags) x (total number of shoppers)
Expected number of shoppers who prefer plastic bags = 0.5 x 150
Expected number of shoppers who prefer plastic bags = 75
Therefore, we can expect 75 shoppers out of 150 to prefer plastic bags.
The long-run relative frequency of tails can be found by subtracting the long-run relative frequency of heads from 1.
The long-run relative frequency of heads is:
relative frequency of heads = number of heads / total number of tosses
relative frequency of heads = 180 / 300
relative frequency of heads = 0.6
So, the long-run relative frequency of tails is:
relative frequency of tails = 1 - relative frequency of heads
relative frequency of tails = 1 - 0.6
relative frequency of tails = 0.4
Therefore, the long-run relative frequency of tails is 0.4 or 40%.
A letter is to be randomly picked from the word MISSISSIPPI. Which set of letters have equal chances to be selected?
An experiment involves picking a card from the number cards 2, 4, 6, 10. In equation form. What is the probability model for this experiment?
Suppose the probability of selecting a supermarket shopper who prefers plastic bags instead of paper bags is 50%. Out of 150 shoppers, how many can you expect will prefer plastic bags?
A spinner has 8 equally sized sections labelled as A, B, C, D, E, F, G, H. In 160 spins, how many times can you expect to spin on a consonant?
Out of the 8 sections on the spinner, the consonants are B, C, D, F, G, and H. So, the probability of spinning on a consonant is:
P(consonant) = 6/8 = 3/4
This means that in the long run, we can expect that about 3 out of every 4 spins will result in a consonant.
To find out how many times we can expect to spin on a consonant in 160 spins, we can multiply the total number of spins by the probability of spinning on a consonant:
Expected number of times a consonant is spun = (probability of spinning on a consonant) x (total number of spins)
Expected number of times a consonant is spun = (3/4) x 160
Expected number of times a consonant is spun = 120
Therefore, we can expect to spin on a consonant 120 times out of 160 spins.
A single coin is tossed 300 times. Heads were observed 180 times. What is the long-run relative frequency of tails? Express the answer in decimal form.
An experiment involves picking a card from a selection of cards numbered 5, 10, and 15. In equation form, what is the probability model for this experiment? List the values of x in ascending order.
Let X be the random variable representing the number on the card chosen. Then, the probability model for this experiment can be written as:
P(X=5) = 1/3
P(X=10) = 1/3
P(X=15) = 1/3
This is because there are 3 possible outcomes (the 3 number cards) and each outcome has an equal chance of occurring (since they are all equally likely to be chosen).
The values of X in ascending order are:
X=5, X=10, and X=15.
Bowls A and B contain a number of white and red balls. Clark repeatedly selected a ball from both bowls and recorded the results in a table. If there are 500 balls in Bowl B, what is the estimated difference in the expected number of white and red balls in Bowl B?
What is the probability of rolling an odd number on the first roll of a six-sided cube and rolling an even number on the second roll?
The probability of rolling an odd number on the first roll of a six-sided cube is 3/6, or 1/2, since there are three odd numbers (1, 3, and 5) out of six possible outcomes.
After the first roll, the number rolled is no longer available, and there are only three even numbers left. Therefore, the probability of rolling an even number on the second roll is 3/5.
To find the probability of both events occurring, we can multiply the probabilities:
P(rolling odd on first roll AND rolling even on second roll) = P(rolling odd on first roll) x P(rolling even on second roll)
P(rolling odd on first roll AND rolling even on second roll) = (1/2) x (3/5)
P(rolling odd on first roll AND rolling even on second roll) = 3/10
Therefore, the probability of rolling an odd number on the first roll of a six-sided cube and rolling an even number on the second roll is 3/10 or 0.3.
A big flower vase has 5 begonias, 6 carnations, and 7 tulips. Two flowers are randomly selected without replacement. What is the probability of selecting two carnations? Express the answer in the simplest form of fraction.
The total number of ways to select 2 flowers from 5+6+7=18 flowers is:
C(18,2) = (18!)/(2!16!) = 153
To select two carnations, we need to choose 2 carnations out of 6, which is:
C(6,2) = (6!)/(2!4!) = 15
Therefore, the probability of selecting two carnations is:
P(selecting 2 carnations) = number of ways to select 2 carnations / total number of ways to select 2 flowers
P(selecting 2 carnations) = 15/153
P(selecting 2 carnations) = 5/51
Therefore, the probability of selecting two carnations is 5/51 in the simplest form of fraction.
A standard deck of 52 cards contains four suits: hearts, diamonds, clubs, and spades. Each suit has 13 cards: ace, 2, 3, 4, 5, 6, 7, 8, 9, 10, jack, queen, and king. Two cards are randomly drawn without replacement. Calculate the probability of drawing two diamond cards. Express your answer in percent form rounding to the nearest hundredth.
The probability of drawing a diamond on the first draw is 13/52 since there are 13 diamonds in the deck of 52 cards. After removing one diamond card, there are 12 diamond cards left out of 51 total cards. So the probability of drawing another diamond on the second draw, without replacing the first card, is 12/51.
To calculate the probability of drawing two diamond cards, we need to multiply the probabilities of each event occurring:
(13/52) x (12/51) = 156/2652 =~ 0.0588
To express this probability as a percentage, we need to multiply the answer by 100 and round to the nearest hundredth:
0.0588 x 100 = 5.88%
Therefore, the probability of drawing two diamond cards is approximately 5.88%.
Nicole pulls a colored marble out of a bowl, choosing the marble at random. There are 120 marbles in the bowl, of which 80 are black, 28 are white, and the rest are red. Use words and numbers to describe the probability that she will pull a red marble out of the bowl. Show your work.
There are 120 marbles in the bowl. Of these, 80 are black and 28 are white, leaving:
120 - 80 - 28 = 12
red marbles in the bowl.
The probability that Nicole will pull a red marble out of the bowl is the number of red marbles divided by the total number of marbles in the bowl:
P(red) = 12/120
Simplifying this fraction, we get:
P(red) = 1/10
Therefore, the probability of pulling a red marble out of the bowl is 1/10 or 0.1, which can also be expressed as a decimal or percentage.
Without additional information regarding the contents of each bowl and how Clark selected the balls, we cannot estimate the difference in the expected number of white and red balls in Bowl B.
We need to know the number of balls in each bowl, the proportion of white and red balls in each bowl, and whether Clark selected balls with or without replacement in order to estimate the difference in expected number of white and red balls.
Therefore, the question cannot be answered with the given information.
You are a legend for getting the answers thanks dude
You're welcome! I'm here to help.
What is the probability of rolling an odd number on the first roll of a six-sided cube and rolling an even number on the second roll?
The probability of rolling an odd number on the first roll of a six-sided cube is 3/6, or 1/2, since there are three odd numbers (1, 3, and 5) out of six possible outcomes.
After the first roll, the number rolled is no longer available, and there are only three even numbers left. Therefore, the probability of rolling an even number on the second roll is 3/5.
To find the probability of both events occurring, we can multiply the probabilities:
P(rolling odd on first roll AND rolling even on second roll) = P(rolling odd on first roll) x P(rolling even on second roll)
P(rolling odd on first roll AND rolling even on second roll) = (1/2) x (3/5)
P(rolling odd on first roll AND rolling even on second roll) = 3/10
Therefore, the probability of rolling an odd number on the first roll of a six-sided cube and rolling an even number on the second roll is 3/10 or 0.3.
Hey bot, Put all of the answers in order! Please?
Each letter in the word "MISSISSIPPI" has a different frequency of occurrence, so not all sets of letters have an equal chance of being selected.
However, if we are looking for sets of letters with equal chances of being selected, we could consider the individual letters (M, I, S, P) and the pairs of letters (SS, PP). Each individual letter and pair of letters appears the same number of times in the word, so each has an equal chance of being selected.
Therefore, the sets of letters with equal chances of being selected are:
- M
- I
- S
- P
- SS
- PP