Question

In: Statistics and Probability

The City Transit Authority plans to hire 14 new bus drivers. From a group of 100...

The City Transit Authority plans to hire 14 new bus drivers. From a group of 100 qualified applicants, of whom 60 are men and 40 are women, 14 names are to be selected by lot. Suppose that Mary and John Lewis are among the 100 qualified applicants.

(a) What is the probability that Mary's name will be selected?

What is the probability that both Mary's and John's names will be selected? (Round your answer to four decimal places.)

(b) If it is stipulated that an equal number of men and women are to be selected (7 men from the group of 60 men and 7 women from the group of 40 women), what is the probability that Mary's name will be selected? (Round your answer to four decimal places.)

What is the probability that Mary's and John's names will be selected? (Round your answer to four decimal places.)

Solutions

Expert Solution

Answer :

given data :-

he City Transit Authority plans to hire new bus drivers =14

a group of qualified applicants = 100

whom 60 are men and 40 are women, 14 names are to be selected by lot

(a) . Now we need to find out the probability that Mary's name will be selected ?

There are 100 candidates, and 14 drivers must be chosen.

Along these lines,

the probability that Mary's name is chosen is = ( 14/100)

= 0.14.

Out of 100 candidates,

if 14 drivers are chosen, the likelihood that John is one of the 14 drivers is 0.14.

In this way, likelihood that both Mary and John are chosen are = ( 0.14 * 0.14 )

= 0.0196

(b) . In the event that 7 ladies are to be chosen from 40 ladies,

at that point probability that Mary's name is incorporated is = ( 7/40 )

= 0.175

Equally, out of 60 men, if 7 are to be chosen,

likelihood that John's name is incorporated is = ( 7/60 )

    = 0.1166

In this way, likelihood that both Mary's and John's names will be chosen is = 7/60 * 7/40

= 0.1166 * 0.175

= 0.0204


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