# Math

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Two cards are drawn from an ordinary deck of 52 playing cards with replacement. What is the probability that A) both cards are the same color? B) both cards are from the same suit? C) How would your answers to parta (a) and (b) change if the draws are made without replacement?

• Math -

A) half of the cards are red and half are blue. The probability is 1/4 that both are read and 1/4 that both are black. Add those and you get 1/2
B) Follow the same logic. Both cubs = 1/4. Both hearts = 1/4 etc. Add them up
C) What do tou think?

• Math -

So would the answer to B)= 1/2.

• Math -

1/2 for (B) is not correct.

"B) Follow the same logic. Both cubs = 1/4. Both hearts = 1/4 etc. Add them up "
Means you'd have to do some calculations for each of the 4 suits.
First club = 13/52
Second club = 13/52 (with replacement)
So both clubs would be 13/52*13/52=1/16
Same goes for each of the other three suits.
Add up the numbers for all four suits and you'll get the required answer.

• Math -

C) Without replacement, the chance of getting the same color on two consecutive draws equals the probability of getting red twice in a row PLUS the probability of getting black twice in a row. That probability is 2*(1/2)*(25/51) = 25/51

The probability of getting two of the same suit in consecutive draws is
4*(1/4)*(12/51)= 12/51
The number 4 in front is due to the fact that there are four different suits; it could be any of them.

• Math -

3. From a deck of 52 ordinary playing cards, two cards are drawn with replacement. Find the probability that both are hearts.

• Math -

it would be 27/625

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