Answer: a) 0.1095 b) 0.0095
Step-by-step explanation:
Given : The deck for a card game contains 30 cards.
10 are red, 10 yellow, 5 blue, and 1 green, and 4 are wild cards.
Each player is randomly dealt a five-card hand.
Number of ways to choose 5 cards out of 30 = [tex]C(30,5)=\dfrac{30!}{5!25!}=142506[/tex]
a) Cards other than wild card = 30-4=26
Number of ways to choose exactly two wild cards = [tex]C(26,3)\timesC(4,2)[/tex]
[tex]=\dfrac{26!}{3!23!}\times\dfrac{4!}{2!2!}\\\\=15600[/tex]
Probability that a hand will contain exactly two wild cards = [tex]\dfrac{15600}{142506}=0.1095[/tex]
b) Number of ways to choose two wild cards, two red cards, and one blue cards = [tex]C(4,2)\times C(10,2)\times C(5,1)[/tex]
[tex]=\dfrac{4!}{2!2!}\times\dfrac{10!}{2!8!}\times5=1350[/tex]
Probability that a hand will contain two wild cards, two red cards, and one blue cards = [tex]\dfrac{1350}{142506}=0.0095[/tex]
