Suppose that you select 2 cards without replacement from a standard deck of 52 p

Question

Suppose that you select 2 cards without replacement from a standard deck of 52 playing cards. If the first card that you select is a club, what is the probability that the second card that you select is a five? Suppose that you select 2 cards without replacement from a standard deck of 52 playing cards. If the first card that you select is a club, what is the probability that the second card that you select is a five? Suppose that you select 2 cards without replacement from a standard deck of 52 playing cards. If the first card that you select is a club, what is the probability that the second card that you select is a five?

Explanation / Answer

Total no. of cards=52

Now we have to select 2 cards without replacement.

First card we draw, it is a club.

Now no. of remaining card=52-1=50

Means second card we draw out of 50 cards

Now there are two cases:

first it may be possible that first card which we have drawn is a five(club), in this case we have only 3 fives out of 50 cards, then the probability that the second card that we select is a five= 3/50

Second case, It may be possible that first card which we have drawn is not a five, in this case we have 4 fives out of 50 cards., then the probability that the second card that you select is a five= 4/50

Thus the final probability is addition of both cases.(When there is a case of "OR" then we add the probabilities)

Hence, the probability that the second card that you select is a five=3/50+4/50=7/50

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