Consider the following in respect of two events A and B : 1. P(A occurs but not B ) `= P(A) - P(B)` if ` B sub A`. 2. P(A alone or B alone occurs)` =P(A)+P(B)-P(AnnB)`. 3. `P(A uu B) = P(A) +P(B)` if A and B are mutually exclusive . Which of the above is/are correct?

Options

A. 1 only
B. 1 and 3 only
C. 2 and 3 only
D. 1 and 2 only

Answer

B

Explanation

Statement 1 : If ` B sub A`, then
`P(A- B) = P(A) - P(Ann B)` .
`= P(A) - P(B)`
`therefore` It is correct.
Statement 2 , P(A alone or B alone).
`P(A) -P(A nn B) +P(B) - P(A nn B)`
` = P(A) + P(B) - 2P(-AnnB)`.
`therefore` It is false .
Statement 3: If A, B are mutually exclusive events , then `P(A nn B) = 0`
`rArr P(A nn B)= 0`.
`rArr P(A nn B) = P(A) +P(B)`.
It is correct.