Use the following information to answer the next two exercises. The percent of licensed U.S. drivers (from a recent year) that are female is \(48.60\). Of the females, \(5.03%\) are age \(19\) and under; \(81.36%\) are age \(20–64; 13.61%\) are age \(65\) or over. Of the licensed U.S. male drivers, \(5.04%\) are age \(19\) and under; \(81.43%\) are age \(20–64; 13.53%\) are age \(65\) or over.

Compute the following:

a. Construct a table or a tree diagram of the situations.

b. Find \(P\)(driver is female)

c. Find \(P\)(driver is age \(65\) or over|driver is female).

The percent of licensed U.S driver that are female is \(48.60\). Of the females \(5.03%\) are age \(19\) and under, \(81.36%\) are age \(20-64 ,13.61%\) are age \(65\) or over. Of the licensed U.S male drivers, \(5.04%\) are age \(19\) and under, \(81.43%\) are age \(20-64 ,13.53%\) are age \(65\) or over.

The table representation is as follows:

The table representation is as follows:

From above table, the probability the driver is female is given as

\(P\)(driver is female)\(=0.486\)

The table representation is as follows:

From above table, we have

\(P\)(driver is female)\(=0.486\)

The probability the driver is age 65 or above given that the driver is female is given as

\(P\)(driver is age \(65\) or above| driver is female)\(=\frac{0.0661}{0.486}\)

\(P\)(driver is age \(65\) or above| driver is female)\(=0.1361\)