Question

Jacob is leaving his house to go to work and running 5 minutes late in the past, when Jacob has been 5 minutes late for work, he has taken an alternate route to work a total of 16 times. When in the same position, Jacob has take his normal route to work 27 times In the situations when Jacob has taken the alternate route to work, he has been late 8 times , on-time 3 times and early 5 times In situations when he has taken his normal route to work, he has been late 9 times on-time 12 times, and early 6 times Based on the information above, if Jacob's goal to be on -time or early for workshould he take the alternate route or his normal route?

Answer 1

Jacob should take the normal route

Explanation:

The given parameters are;

How late is Jacob running for work = 5 minutes

The number of times Jacob has taken the alternative route to work = 16 times

The number of times Jacob has taken the normal route to work = 27 times

The number of times Jacob has been late when he takes the alternative route to work = 8 times

The number of times he has been on-time = 3 times

The number of times he has been early = 5 times

By taking the normal route;

The number of times he has been late = 9 times

The number of times he has bee on-time = 12 times

The number of times he has been early = 6 times

Therefore, we have;

The probability that Jacob will be on-time or early when he takes the alternative route. P(A) = (3 + 5)/16 = 0.5

The probability that Jacob will be on-time or early when he takes the normal route, P(N) = (12 + 6)/27 = 0.
`\overline 6`

Therefore, given that the probability that Jacob will arrive on-time or early when he takes the normal route is higher than the probability when he takes the alternative route, Jacob should take the normal route.