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Find the probability of exactly twosuccesses in five trials of a binomialexperiment in which the probability ofsuccess is 50%.Round to the nearest telth of apercent.

Find the probability of exactly twosuccesses in five trials of a binomialexperiment-example-1
User Stratis
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1 Answer

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Answer

The answer = 0.3125 or 31.25% = 31.3% to 1 decimal place.

Step-by-step explanation

A binomial experiment is one in which the probability of success doesn't change with every run or number of trials.

It usually consists of a number of runs/trials with only two possible outcomes, a success or a failure.

The outcome of each trial/run of a binomial experiment is independent of one another.

Binomial distribution function is represented by

P(X = x) = ⁿCₓ pˣ qⁿ⁻ˣ

n = total number of sample spaces/trials = 5

x = Number of successes required = 2

p = probability of success = 50% = 0.50

q = probability of failure = 1 - p = 1 - 0.50 = 0.50

P(X = 2) = ⁵C₂ (0.50)² (0.50)⁵⁻²

= (5!/3!2!) (0.25) (0.125)

= 10 (0.25) (0.125)

= 0.3125 or 31.25%

Hope this Helps!!!

User Halt
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