To find this probability, you need to:
Recall the binomial distribution formula P(X = r) = nCr × pʳ × (1-p)ⁿ⁻ʳ. We'll use it with the following data:
Number of trials: n = 5;
Number of successes: r = 3; and
Probability of success: p = 0.5.
Calculate 5 choose 3: nCr = 10.
Plug these values into the formula:
P(X = 3) = 10 × 0.5² × 0.5³ = 0.3125.
The probability you're looking for is 31.25%.
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