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gitika · May 2, 2009, 02:29 AM

Two cards are picked at random from a pack of 52 playing cards with replacement. Calculate the probability that these cards are picked:

a. Two kings
b. A red card and a black card
c. A picture card and an odd number card
d. A heart and a diamond

Perito · May 2, 2009, 06:33 AM

a. Since you replace the cards, then each drawing you are picking one out of 52 cards. There are four cards in the deck so each pick has a probability of 4/52 of being a king.

$\frac {4}{52}=\frac {2}{13}$

Since the selection of one card has no affect or influence on the selection of the second card, they are independent events. The probability of selecting one king for each selection is the same. For independent events, you multiply the probabilities to get the final probability. Therefore

$P=\frac {1}{13} \,\times\, \frac {1}{13}\,=\,\frac {1}{169}$

You do the other problems the same way.