Answered

A card is chosen from a standard deck of
cards, its suit is noted and then the card is replaced. A second card is drawn and its suit is noted.

What is the probability of both cards being the same suit? (note: answer is 1/4 - not sure how they got to it)



Answer :

MathPhys

Answer:

1/4

Step-by-step explanation:

There are 52 cards in a standard deck, divided into 4 equal suits of 13 cards per suit.

Notice it doesn't matter what suit the first card is. We only want to know the probability that the second card is the same suit. If the first card is hearts, there's a one in four probability that the second card is also hearts. If the first card is diamonds, there's a one in four probability that the second card is also diamonds. Etc., etc.

We can also show this by calculating the probability for each suit, then finding the total probability.

P(both hearts) = 1/4 × 1/4 = 1/16

P(both diamonds) = 1/4 × 1/4 = 1/16

P(both clubs) = 1/4 × 1/4 = 1/16

P(both spades) = 1/4 × 1/4 = 1/16

P(same suit) = 1/16 + 1/16 + 1/16 + 1/16 = 1/4

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