A and B are two events defined as follows:
A: It rains today with `P(A)=40%`
B: It rains tomorrwo with `P(B)=50%`
Also, P(it rains today and tomorrow)`=30%`
Also `E_(1):P((AnnB)//(AuuB))and E_(2):P({AnnbarB)or (BuubarA)}//(AuuB)).` Then which of the following is/are true ?

Options

A. `P(A//B)ltP(B//A)`
B. `P(A//B)ltP(B//A)`
C. `E_(1)and E_(2)` are equiprobable
D. `P(A//(AuuB))=P(B//(AuuB))`

Answer

B, C

Explanation

`P(A)=0.4,P(B)=0.5,P(AnnB)=0.3`
`impliesP(AuuB)=P(A)+P(B)-P(AnnB)=0.6`
Now, `P(E_(1))=(P(AnnB))/(P(AuuB))=(0.3)/(0.6)=1/2`
`P(E_(2))=(P(AnnbarB)+P(barAnnB))/(P(AnnB))=(0.1+0.2)/(0.6)=1/2`
`P(A//B)(P(AnnB))/(P(B))=(0.3)/(0.5)=3/5=0.60,`
`P(B//A)=(0.3)/(0.4)=(3)/(4)=0.75`
`P(A//(AuuB))=(P(A))/(P(AuuB))=(0.4)/(0.6)=2/3`
`(P(B))/(P(AuuB))=(0.5)/(0.6)=5/6`