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A library contains 60 books, numbered from 1 to 60. If three books are selected at random and with replacement from the library, what is the probability that the sum of the three numbers on the books selected from the library will be odd?

A library contains 60 books, numbered from 1 to 60. If three books are selected at random and with replacement from the library, what is the probability that the sum of the three numbers on the books selected from the library will be odd? Correct Answer 1/2

Given:

A library contains 60 books, numbered from 1 to 60 and three books are selected at random and with replacement from the library.

Concept used:

The classical definition of probability.

Formula used:

Probability = Favorable Outcome/Total Outcome.

P(E) = n(E)/n(S)

Calculation:

P(odd) = P(even) =1/2     ...(∵ There are 30 odd and 30 even numbers)

Sum or the three numbers can be odd only under the following 4 scenarios:

Odd + Odd + Odd = 1/2 × 1/2 × 1/2 = 1/8

Odd + Even + Even = 1/2 × 1/2 × 1/2 = 1/8

Even + Odd + Even = 1/2 × 1/2 × 1/2 = 1/8

Even + Even + Odd = 1/2 × 1/2 × 1/2 = 1/8

Other combinations of odd and even will give even numbers.

Adding up the 4 scenarios above:

= 1/8 + 1/8 + 1/8 + 1/8

= 4/8

= 1/2

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