The probability of winning exactly 21 times is 0.14

Binomial probability refers to the probability of exactly ‘x’ successes on ‘n’ repeated trials in an experiment which has two possible outcomes (commonly called a binomial experiment).

Probability ‘P’ = ⁿCₓ (probability of 1st)ˣ x (1 – probability of 1st)ⁿ⁻ˣ

For example:

What is the probability of getting 6 heads, when you toss a coin 10 times?

In a coin-toss experiment, there are two outcomes: heads and tails. Assuming the coin is fair , the probability of getting a head is 1/2 or 0.5 .

The number of repeated trials: n=10

The number of success trials: x = 6

The probability of success on individual trial: p = 0.5

Use the formula for binomial probability.

¹⁰C₆ (0.5)⁶ x (1 – 0.5)¹⁰⁻⁶

Simplify.

≈0.205

Here, we have given that:

Probability of winning on an arcade game is 0.659

so, Probability of loosing on an arcade game is 1-0.659 = 0.341

Number of times game played = 30

Probability of winning exactly 21 times = ?

now, n = 30

x = 21

probability of 1st or probability of winning = 0.659

1 – probability of 1st or probability of loosing = 0.341

using, binomial probability formula

Probability of winning exactly 21 times = ³⁰C₂₁ (0.659)²¹ x (0.341)⁷

on solving,

Probability of winning exactly 21 times = 0.14

Hence,

The probability of winning exactly 21 times is 0.14

Learn more about “ Binomial Probability ” from here: https://brainly.com/question/12474772

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