Mbawarrior01
The length of Alice's commute, in minutes, differs depending on whether it's a weekday or weekend.
The probability of how long the weekday commute will take is included in the table below.
0 - 15 Minutes 15 - 30 Minutes 30 - 45 Minutes 45 Minutes or More
0.05 0.25 0.4 0.3
The probability of how long the weekend commute will take is included in the table below.
0 - 15 Minutes 15 - 30 Minutes 30 - 45 Minutes 45 Minutes or More
0.25 0.50 0.15 0.1
If Alice's commute took 30 minutes or less today, what is the probability that today is a weekday? Assume Alice commutes every day and that weekdays are considered to be Monday-Friday.
\(\frac{2}{7}\)
\(\frac{3}{8}\)
\(\frac{3}{7}\)
\(\frac{1}{2}\)
\(\frac{5}{7}\)
I have no clue how to go about this question
P(B given A) = P(A and B)/P(A)
P('Weekday' given '30 mins or less') = P(Weekday and 30 mins or less) / P(30 mins or less)
P(Weekday and 30 mins or less) = (5/7) * 0.3 = 1.5/7
P(30 mins or less) = (5/7) * 0.3 + (2/7) * .75 = 3/7
P('Weekday' given '30 mins or less') = (1.5/7) / (3/7) = 1/2
, I did not get this solution. Can you please help me understand this. Thank you in advance.