# Thread: probability Mr. Smith will miss work

1. ## probability Mr. Smith will miss work

Hi!
Can you hep me with this?

Mr. Smith can drive to work along the shortest path or bypass.
He drives the shortest path in 36% cases. The probabilty he will get stuck in traffic jam
on the shortest road is 20%, in addition in the case of traffic jam he can miss the work with the probability of 10%.
The probability to get stuck in traffic on bypass road is 8%, in addition after getting out of traffic jam, he can
miss work with the probability of 24%.

a) what is the probability, Mr. Smith will miss the work?
b) If Mr. Smith misses work, what is the probability, he was driving bypass road?

Do I have to use full probability, Bayse formula or something else?

2. ## Re: probability Mr. Smith will miss work

Originally Posted by Kiiefers
Hi!
Can you hep me with this?

Mr. Smith can drive to work along the shortest path or bypass.
He drives the shortest path in 36% cases. The probabilty he will get stuck in traffic jam
on the shortest road is 20%, in addition in the case of traffic jam he can miss the work with the probability of 10%.
The probability to get stuck in traffic on bypass road is 8%, in addition after getting out of traffic jam, he can
miss work with the probability of 24%.

a) what is the probability, Mr. Smith will miss the work?
b) If Mr. Smith misses work, what is the probability, he was driving bypass road?

Do I have to use full probability, Bayse formula or something else?
Law of total probability is sufficient. You would like $\displaystyle P(\overline{W})$ where W is the event that Mr.Smith shows to work. Let S be the event that Mr.Smith takes the shortest path.

$\displaystyle P(\overline{W}) = P(\overline{W} | S) P(S) + P(\overline{W} | \overline{S}) P(\overline{S})$

Now, $\displaystyle P(\overline{W} | S) = 0.2(0.1)$ and $\displaystyle P(\overline{W} | \overline{S}) = 0.08(0.24)$, and I'll let you take it from here.

thanks

4. ## Re: probability Mr. Smith will miss work

Originally Posted by majamin
Law of total probability is sufficient. You would like $\displaystyle P(\overline{W})$ where W is the event that Mr.Smith shows to work. Let S be the event that Mr.Smith takes the shortest path.

$\displaystyle P(\overline{W}) = P(\overline{W} | S) P(S) + P(\overline{W} | \overline{S}) P(\overline{S})$

Now, $\displaystyle P(\overline{W} | S) = 0.2(0.1)$ and $\displaystyle P(\overline{W} | \overline{S}) = 0.08(0.24)$, and I'll let you take it from here.
So it will be like this?

P=0,36*0,2*0,1+0,64*0,08*0,24

5. ## Re: probability Mr. Smith will miss work

Yes. That looks correct.