I needed help with 3 remaining probabilities questions from

I needed help with 3 remaining probabilities questions from a homework assignment. Please include steps as well, thank you. The problems are in picture from on this dropbox link: https://www.dropbox.com/sh/njvyn1is272pfqa/AABBz7ypdQ8McIwmOfJzjMQPa?dl=0

Solution

23)
a)P(A/B) = P(A and B)/P(B) = 0.2/0.35 = 0.57
b)P(C/B) = P(C and B)/P(B) = 0.15/0.35 = 0.43
c)P(B/AUC) = P(B and (AUC))/P(AUC) = 0.25/0.7= 0.36
d)P(B/A and C)= P(B and (A and C))/P(A and C) = 0.1/0.2 = 0.5

24)
integral (0->10) xdx
=> x^2/2 (0->10)
=> 50
Therefore,
PDF = x/50
a)
P(2<= X<= 5) = integral ( 2->5) x/50dx
= 1/50 * (x^2/2) (from 2->5)
= 1/50 * 1/2 * 21
= 0.21 Answer

b)
P(X<=2/ X<= 5) = P(X<=2 and X<=5)/P(X<=5)
= P(X<=2)/P(X<=5)
=(integral ( 0->2) x/50dx) / (integral ( 0->5) x/50dx)
= (x^2/2) (from 0->2) / (x^2/2) (from 0->5)
= 4/25
= 0.16 Answer

c)
P(3<=X<=8/ X>= 4) = P(3<=X<=8 and X>=4)/P(X>=4)
= P(4<=X<=8)/P(X>=4)
=(integral ( 4->8) x/50dx) / (integral ( 4->10) x/50dx)
= (x^2/2) (from 4->8) / (x^2/2) (from 4->10)
= (64 - 16)/(100-16)
= 0.57 Answer

25)
Probability of getting an A P1= (120)/600 = 1/5
Probability of living on campus P2= (200)/600 = 1/3
Probability of getting an A and living in campus P3= (12-80)/600 = 1/15

Since P3 = P1*P2
\"getting an A\" and \"living on campus\" are independent.