Home
Class 12
MATHS
Let P(x) denote the probability of the o...

Let P(x) denote the probability of the occurrence of event x. Plot all those point (x y) = (P(A), P(B)) in a plane which satisfy the conditions, `P(A uu B) ge 3//4 and 1//8 le P(A nn B) le 3//8`

Text Solution

Verified by Experts

`P(A uu B) ge (3)/(4) and (1)/(8) le P(A nn B) le (3)/(8)`
Hence,
`P(A) + P(B) - P(A nn B) le (3)/(4)`
implies `P(A) + P(B) ge (3)/(4) + P(A nn B) ge (3)/(4) + (1)/(8) = (7)/(8)`
`implies x + y ge (7)/(8)`
We know that
`P(A nn B) le 1`
`implies P(A) + P(B) le 1 + P(A nn B) le 1 + (3)/(8) = (11)/(8)`
`implies x + y le (11)/(8)`

The shaded part in the figure is the required region.
Promotional Banner

Topper's Solved these Questions

  • PROBABILITY I

    CENGAGE|Exercise Solved Example|1 Videos

  • PROBABILITY I

    CENGAGE|Exercise Exercise 9.1|6 Videos

  • PROBABILITY AND STATISTICS

    CENGAGE|Exercise Question Bank|24 Videos

  • PROBABILITY II

    CENGAGE|Exercise JEE Advanced Previous Year|25 Videos

Similar Questions

Explore conceptually related problems

If A and B are two independent events, then the probability of occurrence of at least one of A and B is given by 1- P(A') P(B').

If for two events A and B , P(A)=(3)/(4), P(B)=(2)/(5) and AuuB=S (Sample space) find the conditional probability P(A//B)

If A and B are two events such that P(A nn B) = 7/10 and P(B) 17/20 , then P(A/B) =

If for two events A and B, P(A) = 3/4, P(B) = 2/5 and A uu B = S (sample space), find the conditional probability P(A/B).

If Aa n dB are two events, the probability that exactly one of them occurs is given by a. P(A)+P(B)-2P(AnnB) b. P(Ann B )+P( A nnB) c. P(AuuB)-P(AnnB) d. P( A )+P( B )-2P( A nn B )

If A and B are two events such that P(A) = 0.4, P(B) = 0.8 and P(B//A) = 0.6 , then P(barA nn B) is

If two events A and B are such that P (barA) = 3/10 and P(A nn barB) = 1/2 , then P(A nn B) is

If P(A)=0.5, P(B)=0.8 and P(B//A)=0.8 find P(A//B) and P(A uu B)