Number of diamonds = 13
Total number of cards = 52
P[ a diamond is drawn ] = 12/52 = 1/4
Number of total cards drawn = 15
this is a case of binomial distribution with p = 0.25 and n = 15
P[ At least 5 diamond ] = 1 - P[ X <= 4 diamonds ]
Therefore, we get that
This implies that
P[ X <= 4 diamonds ] = 0.6865
P[ At least 5 diamond ] = 1 - P[ X <= 4 diamonds ]
P[ At least 5 diamond ] = 1 - 0.6865
P[ At least 5 diamond ] = 0.3135
E(X) = np = 0.25*15 = 3.75
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