You can
put this solution on YOUR website!First of all, the statement describing the experiment is ambiguous. Are you drawing one card and it must be exactly the 5 of spades, or are you drawing two cards, one of which must be a 5 and the other must be a spade? Furthermore, you don't specify if, on a two card draw, whether you are replacing the first card before making the second draw.
Case 1: One card draw and success = 5 of spades. Trivial. There is only one 5 of spades in the deck, so your probability is
Case 2: Two card draw with replacement and success = one card will be a spade of any rank and the other will be a 5 of any suit.
First of all, there are 13 spades out of 52 cards, so the probability of drawing any spade is
.
Second, there are four 5s in the deck, so the probability of drawing a 5 is
And the total probability is the product
, approximately 0.019 or 1.9%
Case 3: Two card draw WITHOUT replacement and success is the same as Case 2.
You have to consider the possibility that the first card drawn is the 5 of spades. So:
Case 3a: The probability of drawing a spade other than the 5 times the probability of drawing a 5 when the deck is one card smaller
Plus
Case 3b: The probability of drawing the 5 of spades times the probability of drawing a 5 with a deck that is one card smaller AND has one less 5
Total probability
roughly the same value as Case 2.
Case 4: You really meant to ask "What is the probability, on a one card draw, that the card will be a spade OR a 5"
Again 13 spades and 4 fives one of which is a spade and already counted, so there are 3 other suited fives, making a total of 16 cards that represent a successful experiment, and your probability is
(You could also look at it as 4 fives and 12 spades that aren't a five adding up to the same 16 successes out of 52 possibilities.)
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