Using the principle of binomial probability, the probability of having exactly two black cards is 0.3125
- Probability of having a black card = 26/52 = 1/2
Using the binomial probability relation :
- P(x = x) = nCx * p^x * q^(n-x)
- p = probability of success = 1/2 = 0.5
- Number of picks, n = 5
- q = 1 - p = 0.5
- x = 2
Hence,
P(x = 2) = 5C2 × 0.5² × 0.5³
P(x = 2) = 10 × 0.25 × 0.125
P(x = 2) = 0.3125
Hence. Probability of having exactly 2 black cards is 0.3125
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