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3. Twenty percent (20%) of the customers of a store buy cigars. Half of the customers who buy cigars buy beer. About 45 percent buy beer. The table is given below:

Cigar\Beer Buy Beer No Beer Total

Buy Cigar 0.10 0.20

No Cigar

Total 0.45

A customer is known to not buy beer. Determine the probability that this customer will buy Cigar.

Sagot :

Answer:-

0.181818

Solution:-

By the problem, it is given that 20% of the coustomers of a store buy cigars.Half of the customers who buy cigars buy beer.About 45% buy beer.

A customer is known to not buy beer.Need to find the probability that this customer will buy cigar.

The table for necessary calculation-

             Beer    No beer     Total

Cigar 0.10       0.10            0.20

No cigar 0.35 0.45 0.80

Total 0.45 0.55 1

Need to find the probability -

P[The customer will buy cigar | The customer is known to not buy beer]

Using the Theorem of conditional probability,

=0.10/0.55

=0.181818

Hence, the required probability is 0.181818.

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