SOLUTION: A box has five blocks numbered 3, 4, 5, 6, 7 in it. Two times a block is drawn at random and with replacement (this means the block is put back in the box after it had been drawn).

Algebra ->  Probability-and-statistics -> SOLUTION: A box has five blocks numbered 3, 4, 5, 6, 7 in it. Two times a block is drawn at random and with replacement (this means the block is put back in the box after it had been drawn).      Log On


   



Question 1184359: A box has five blocks numbered 3, 4, 5, 6, 7 in it. Two times a block is drawn at random and with replacement (this means the block is put back in the box after it had been drawn). Calculate the probability that at least one of the blocks drawn had an odd number on it. (Give the answer as a fraction in lowest terms.)

Answer by ikleyn(52812) About Me  (Show Source):
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A box has five blocks numbered 3, 4, 5, 6, 7 in it. Two times a block is drawn at random and with replacement
(this means the block is put back in the box after it had been drawn). Calculate the probability that at least one
of the blocks drawn had an odd number on it. (Give the answer as a fraction in lowest terms.)
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The probability to draw an even block in first draw is  2%2F5.


The probability to draw an even block in second draw is  2%2F5, again.


The probability to draw an even block in both first and the second draw is  %282%2F5%29%5E2.


The probability to get at least one of the blocks drawn an odd number is the COMPLEMENT to  %282%2F5%29%5E2


    P = 1 - %282%2F5%29%5E2 = 1 - 4%2F25 = 21%2F25.    ANSWER

Solved.