Bill commutes to work in the business district of Boston. He takes the train 3/5 of the time and drives 2/5 of the time (when he visits clients). If he takes the train, then he gets home by 6:30 p. m. 83% of the time; if he drives, then he gets home by 6:30 p. m. 62% of the time. If Bill gets home by 6:30 p. m., what is the probability that he drove to work? (Round your answer to three decimal places.)

The probability that Bill drove to work given that he reached home by 6:30 PM is 0.3324.

Step-by-step explanation:

Denote the events as follows:

T = Bill takes the train to work

D = Bill drives to work

X = Bill gets home from work by 6:30 PM.

The information provided is:

P (T) = 0.60

P (D) = 0.40

P (X|T) = 0.83

P (X|D) = 0.62

The Bayes's theorem states that the conditional probability of an event Ei given that another event has already occurred is:

Use the Bayes' theorem to determine the value of P (D|X) as follows:

Thus, the probability that Bill drove to work given that he reached home by 6:30 PM is 0.3324.

2. angles qrt and qst both measures 156 degrees.

step-by-step explanation:  

we have been given a diagram of a circle and we are told that measure of arc qvt is 156 degrees.  

we can see from our given diagram that angle qrt and angle qst subtends to arc qvt.

since we know that angles subtended by the same arc at the circumference are always equal.

by angle subtended by same arc theorem, measure of angle qrt and angle qst will be equal to the measure of arc qvt.

therefore, angles qrt and qst both measures 156 degrees and 2nd statement is the correct choice.