Question

a five-card hand is dealt at random from a standard deck. What is the probability that the hand contains exactly two black cards

Answer 1

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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