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.
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.
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%.