In: Statistics and Probability
A = Event that Tom's number is greater than Jim's number.
B = Event that Tom's number is divisible by 5.
So, we have to find P ( A|B) = P ( A B) / P ( B)
A B = Event that Tom's number is divisible by 5 and it is greater than Jim's number
= (Tom's number is 5 , Jim's number is any number from 1 to 4) ( Tom's number is 10 , Jim's number is any number from 1 to 9) ( Tom's number is 15 , Jim's number is any number from 1 to 14)
Total number of cases in A B is = 4+9+14 = 27
Tom select any number in 15 ways and for every 15 numbers of Tom, Jim can select numbers in 14 was. Total cases = 15*14 = 210
So, P(A B )= 27 / 210
P(B) = P( Tom select 5 or 10 or 15 from list of 15 numbers ) = 3 /15 =1/5
So,
P ( A|B) = (27/210) / ( 1/5 ) = 9/14 or 0.643
Given that Tom’s number is divisible by 5, the probability that Tom’s number is greater than Jim’s number is 9/14 or 0.643
If you find my answer useful then please support me by putting thumbs-up.Thank you.