Question

The probability of getting a single pair in a poker hand of five cards is approximately 0.42. Find the approximate probability that out of 990 poker hands, there will be at least 450 with a single pair.

Note: we didn’t cover the continuity correction in class, and you shouldn’t use it.

?(more than 450 out of 990 hands have a single pair)≈

Answer 1

X ~ Bin ( n , p)

Where n = 990 , p = 0.42

Mean = n p = 990 * 0.42 = 415.8

Standard deviation = sqrt ( n p( 1 - p) ) = sqrt ( 990 - 0.42 ( 1 - 0.42) ) = 15.5295

Using normal approximation,

P(X > x) = P(Z > ( x - mean) / SD )

So,

P(X > 450) = P(Z > ( 450 - 415.8) / 15.5295 )

= P(Z > 2.20)

= 0.0139 (From Z table)