Determine the probabilities You randomly select 7 cars from a regular deck. a. W
ID: 3223579 • Letter: D
Question
Determine the probabilities
You randomly select 7 cars from a regular deck.
a. What is the probability that you have two pair?
b. What is the probability that you have three pair?
c. What is the probability that you have a “full house” which 4 of kind and3 of kind.
You have a bag with 13 ping pong balls that are numbered 1 through 13. You randomly select three balls.
a. If you select with replacement, what is the probability that the sum of the three numbers you select is Even?
b. If you select without replacement (or take three out at once) what is the probability that the sum of the three numbers is even?
Explanation / Answer
slecting 7 cards from a regular deck
a)
no of ways to select 7 cards from deck = 52C7 = 133784560
no of ways of getting two pair = no of ways of slecting 2 ranks for getting two pairs and 3 cards from rest for getting 3 single cards = (13C2*(4C2)*(4C2))(11C3) = 463320
probability that you have two pair = 463320/133784560 = 0.003463
b)
no of ways of getting three pair = no of ways of slecting 3 ranks for getting 3 pairs and 1 rank from rest for getting 1 single card t= (13C3*(4C2)*(4C2)*(4C2))(11C1) = 679536
probability that you have three pair = 679536/133784560 = 0.00508
c)
no of ways to get full house = slecting 1 rank for 4 of kind and other rank for getting 3 of kind
= (13*(1))*(12*(4C3)) = 624
probability that you have a “full house” = 624/133784560 = 0.000004664
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