The deck for a card game is made up of 108 cards. Twenty-five each are red, yellow, blue, and green, and eight are wild cards. Each player is randomly dealt a seven-card hand.

(a) What is the probability that a hand will contain exactly two wild cards?

(b) What is the probability that a hand will contain two wild cards, two red cards, and three blue cards?

a. 0.076

b. 0.000693

Step-by-step explanation:

From the definition of probability,

P (event) = possible outcome of event / total probability

Since from the question the total Of 108 cards with 7 different combinations of cards which can be, hence we have

C (108,7)

Also from the 7 wild cards we can have 2 different combinations, this give

C (7,2)

and there are 5 different combinations from the remaining 100 cards C (100,5)

Hence the desire probability is

(C (100,5) * C (7,2) / C (108,7))

0.076

b. since there are 8 wild cards we have C (8,2), 25 red cards C (25,2) and 25 blue cards C (25,2)

Hence the desired probability is

((C (8,2) * C (25,2) * C (25,2)) / C (108,7))

0.000693