Home
Class 12
MATHS
For two given events A and B,P(A cup B) ...

For two given events A and B,`P(A cup B)` is

A

not less than P(A)+P(B)-1

B

not greater than P(A)+P(B)

C

equal to `P(A)+P(B)-P(A cup B)`

D

equal to P(A)+P(B)+P(A cup B)

Text Solution

Verified by Experts

The correct Answer is:
A, B, C
We know that,
`P(AnnB)=P(A)+P(B)-P(AuuB)`
Also, `P(AuuB)le1`
`:. P(AnnB)_(min)," where "P(AuuB)_(max)=1`
`rArr P(AnnB)geP(A)+P(B)-1`
`:.` Option (a) is true.
Again, `P(AuuB)ge0`
`:. P(AnnB)_(max)," when "P(AuuB)_(min)=0`
`rArr P(AnnB)le P(A)+P(B)`
`:. `Option (b) is true.
Also, `P(AnnB)=P(A)+P(B)-P(AuuB)`, Thus, (c ) is also correct.
Hence, (a),(b),(c ) are correct options.
Promotional Banner

Topper's Solved these Questions

  • PROBABILITY

    IIT JEE PREVIOUS YEAR|Exercise TOPIC 2 ADDITION AND SUBTRACTION LAW OF PROBABILITY OBJECTIVE QUESTION II (ONE OR MORE THAN ONE CORRECT OPTION )|1 Videos

  • PROBABILITY

    IIT JEE PREVIOUS YEAR|Exercise TOPIC 2 ADDITION AND SUBTRACTION LAW OF PROBABILITY OBJECTIVE QUESTION II (FILL IN THE BLANKS )|2 Videos

  • PROBABILITY

    IIT JEE PREVIOUS YEAR|Exercise TOPIC 1 CLASSICAL PROBABLITY OBJECTIVE QUESTIONS (ANALYTICAL AND DESCRIPTIVE QUESTIONS )|5 Videos

  • PERMUTATIONS AND COMBINATIONS

    IIT JEE PREVIOUS YEAR|Exercise Dearrangement and Number of Divisors (Fill in the Blank )|1 Videos

  • RELATIONS AND FUNCTIONS

    IIT JEE PREVIOUS YEAR|Exercise All Questions|1 Videos

Similar Questions

Explore conceptually related problems

For two given events A and B P(A nn B) =

For two given event A and B, P(AcapB) is

If A and B are two given events, then P(A cap B) is

For two independent events A and B, what is P(A+B), given P(A)=3/5 and P(B)=2/3

For two events A and B,P(B)=0.3,P (A but not B)=0.4 and P(notA)=0.6. The events A and B are

If A' , B' are complementary events of two independent events A, B, then P(Acup B) =

For two events, A and B, it is given that P(A) = (3)/(5), P(B) = (3)/(10) , and P(A|B)= (2)/(3) . If bar(A) and bar(B) are the complementary events of A and B, then P(bar(A) |bar(B)) equal to ?