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1) Pick two cards Randomly from an ordinary deck (52 cards). Find the probabilit

ID: 3201678 • Letter: 1

Question

1) Pick two cards Randomly from an ordinary deck (52 cards). Find the probability that:

a: two cards are all hearts

b: two cards are from different suits (say, one is heart, one is diamond)

2) Pick four cards randomly from an ordinary deck (52 cards). Find the probability that:

a: Among them, three hearts and one club.

b: All are from the same suit.

c: There are two distinct pairs (like 2288)

3) In our class, there are 14 female and 11 male students. among them, there are 8 students who get grade 'A'. Among these 'A' students, 5 are female.

a: How many male students who do not get grade 'A'?

b: How many female students who do not get grade 'A'?

Explanation / Answer

1) Pick two cards Randomly from an ordinary deck (52 cards). Find the probability that:
a: two cards are all hearts
we have 13 heart cards in a pack of 52
p(picking up 2 heart cards) = 13 C 2 / 52 C 2 = nCr(13,2)/nCr(52,2) = 0.05882


b: two cards are from different suits (say, one is heart, one is diamond)
two cards are from diffrent suit = 1 - [ 4 * (2 cards are from same suit) ]
= 1 - [ 4 * nCr(13,2)/nCr(52,2) ] = 1 - [ 4 * 0.05882 ] = 0.76472