One drawer in a dresser contains 9 blue socks and 5 white socks. A second drawer...

One drawer in a dresser contains 9 blue socks and 5 white socks. A second drawer contains 5 blue socks and 1 white socks. One sock is chosen from each drawer. What is the probability that they match? Express the answer in decimals.

Expert Solution

ANSWER:

Given that:

One drawer in a dresser contains 9 blue socks and 5 white socks. A second drawer contains 5 blue socks and 1 white socks.

The sample space consists of all pairs of socks — one sock chosen from the first drawer and another one chosen from the second drawer. Each pair is equally likely to be chosen. The event that socks match corresponds to the set of pairs of same color socks_ Therefore.

There are 9 + 5 = 14 socks in the first drawer and 5 +1 = 6 socks in the second drawer. Hence the number of all pairs of socks is ( 14 ) ( 6 ) = 84 .

The number of pairs in which socks match is found by summing the number of pairs of blue socks and the number of pairs of white socks.

Number of pairs of blue socks = ( 9 ) ( 5) = 45.

Number of pairs of white socks = ( 5 ) ( 1 ) = 5.;

socks , the number of matching pairs of socks is 45 + 5 = 50

socks , P ( socks match) = 50 / 84 = 0.5952

orchestra answered 1 year ago

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