Acard is chosen at random from a deck of 52 cards. it is replaced, and a second card is chosen. what is the probability that both cards chosen are clubs? (in fraction simplest form)

The probability that an ace is drawn is 4/52, or 1/13the probability that a heart is drawn is 13/52, or 1/4don't forget that one of the aces is the ace of heartsP(an ace or heart is drawn)=4/52+13/52-1/52P=16/52=4/13or look at it this way...P=13/52+3/52=16/52 because one of the aces, the ace of hearts, is already include in the 13/52you add the probabilities because of the word "or"the odds (in favor) of an ace or a heart is the ratio of the probability that the event will occur to the probability that the event will not occurodds=(16/52)/(36/52)=16/36=4/9, or simply look at 4/13, 13-4=9, and the ratio is 4/9the event cannot happen in 36 ways: 13 diamonds+13 spades+13 clubs-ace of diamonds-ace of spades-ace of clubs=39-3=36, so 16(ways it can happen)/36(ways it cannot happen)=16/36=4/9note: don't be mislead looking at 4/9, it is not probability but odds; the event can happen in 4 ways and cannot happen in 9 ways, so the event can happen in 4 ways out of a total of 4+9=13 ways