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.
The theoretical probability of getting three heads in a single toss of three coins is (1/2)^3 = 1/8.
Out of the 100 times the experiment was carried out, three heads occurred 40 times.
The experimental probability of getting three heads = 40/100 = 2/5.
The difference between the experimental probability and the theoretical probability is:
2/5 - 1/8 = (16/40) - (5/40) = 11/40.
Therefore, the difference between the experimental probability of getting three heads and its theoretical probability is 11/40.
The number cube was rolled 30 times and landed on 3 ten times.
The experimental probability of landing on a 3 is calculated as:
Number of times the cube landed on 3 / Total number of rolls
= 10 / 30
= 1/3
Therefore, the experimental probability of landing on a 3 is 1/3.
We can start by finding the number of red marbles in the bowl:
Number of red marbles = Total number of marbles - (Number of black marbles + Number of white marbles)
Number of red marbles = 120 - (80 + 28)
Number of red marbles = 12
Therefore, there are 12 red marbles in the bowl.
The probability that Nicole will pull a red marble out of the bowl can be found by dividing the number of red marbles by the total number of marbles:
Probability of pulling a red marble = Number of red marbles / Total number of marbles
Probability of pulling a red marble = 12 / 120
Probability of pulling a red marble = 1/10
Expressed as a decimal, this is 0.1 or 10%.
Therefore, the probability that Nicole will pull a red marble out of the bowl is 1/10 or 10%.
What is 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
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?
The consonants are all the letters except A, E, and I, so there are 5 consonants: B, C, D, F, G.
Since the probability of landing on any one section is 1/8, the probability of landing on a consonant is 5/8.
To find how many times we can expect to spin on a consonant out of 160 total spins, we can multiply the probability of landing on a consonant by the total number of spins:
Expected number of spins on a consonant = (5/8) x 160
= 100
Therefore, we can expect to spin on a consonant 100 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
The long-run relative frequency of tails is equal to 1 minus the long-run relative frequency of heads.
In this case, the coin was tossed 300 times and heads were observed 180 times, so tails must have been observed 300 - 180 = 120 times.
The long-run relative frequency of heads is 180/300 = 0.6.
Therefore, the long-run relative frequency of tails is 1 - 0.6 = 0.4.
Expressed as a decimal, the long-run relative frequency of tails is 0.4.
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?
f(x)= [blank], where x=2, 4, 6, 10 @bot
Since there are only four cards to choose from, there are only four possible outcomes:
- If the card picked is 2, then x = 2
- If the card picked is 4, then x = 4
- If the card picked is 6, then x = 6
- If the card picked is 10, then x = 10
Since each card has an equal chance of being picked, the probability of each outcome is 1/4.
Therefore, the probability model for this experiment can be written as:
f(x) = 1/4, where x = 2, 4, 6, or 10.