35.3k views
5 votes
You spin the spinner 20 times.about how many times do you expect it will land on A

1 Answer

5 votes

Answer: 5 times

Step-by-step explanation: The expected value of a random variable is the average value that it would take over many repeated trials. In this case, the random variable is the number of times the spinner lands on A in 20 spins. To calculate the expected value, we need to know the probability of each possible outcome and multiply it by the corresponding value. For example, the probability of landing on A zero times is (3/4)^20, which is about 0.003%, and the value is 0. So we multiply 0.003% by 0 and get 0. Similarly, the probability of landing on A once is 20 x (1/4) x (3/4)^19, which is about 0.016%, and the value is 1. So we multiply 0.016% by 1 and get 0.016%. We do this for all possible outcomes from 0 to 20, and add them up to get the expected value. The formula is:

E(X) = sum of P(X=x) x x for x = 0 to 20

where X is the number of times the spinner lands on A, P(X=x) is the probability of landing on A x times, and x is the possible value.

When we simplify this formula, we get:

E(X) = (1/4) x sum of x for x = 0 to 20

which is equivalent to:

E(X) = (1/4) x (0 + 1 + 2 + … + 20)

Using the formula for the sum of an arithmetic series, we get:

E(X) = (1/4) x (20/2) x (0 + 20)

which simplifies to:

E(X) = (1/4) x 10 x 20

which equals:

E(X) = 5

This means that the expected number of times the spinner lands on A in 20 spins is 5.

Hope this helps, and have a great day! =)

User Iobelix
by
7.9k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories