The probability of winning exactly 21 times is 0.14
<h3>What is Binomial Probability?</h3>
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: brainly.com/question/12474772
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