## Question

### Solution

Correct option is

Both S1 and S2 are true

we are given that

P(A ∩ B) = P(AP(B)

P(B ∩ C) = P(BP(C), P(C ∩ A) = P(CP(A)

and          P(A ∩ ∩ C) = P(AP(B), P(C)

we have

P(A ∩ (∩ C)) = P(A ∩ ∩ C) = P(AP(B), P(C) = P(A)P(B∩ C).

⇒         A and B ∩ are independent. Therefore, S2 is true Also

Also        P[(A ∩ (∪ C)] = P[(A ∩ B) ∪ (∩ C)]

= P[(A ∩ BP(∩ C) – P[(A ∩ B) ∩ (∩ C)]

= P(A ∩ B) + P (A ∩ C) – P(A ∩ ∩ C)

= P(AP(B) + P(AP(C) – P(AP(BP(C)

= P(A) [P(B) + P(C) – P(BP(C)]

= P(A) [P(B) + P(C) – P(∩ C)] = P(AP(∪ C)

∴         A and B ∪ C are independent.

#### SIMILAR QUESTIONS

Q1

A determinant is chosen at random from the set of all determinants of order 2 with elements 0 or 1 only. The probability that the determinant chosen is non – zero is

Q2

A fair coin is tossed 100 times. The probability of getting tails an odd number of times is

Q3

One hundred identical coins, each with probability of head are tossed once. If 0 < p < 1 and the probability of heads showing on 50 coins is equal to that of heads showing on 51 coins, the value of p is

Q4

Suppose X follows a binomial distribution with parameters n and p, where 0 < p < 1. If P (X = r)/P(X = n – r) is independent of n for every value ofr, then

Q5

The minimum number of times a fair coin must be tossed so that the probability of getting at least one head is at least 0.8 is

Q6

For the three events AB and CP(exactly one of the events A or Boccurs) = P(exactly one of the events B or C occurs) = P(exactly one of the events C or A occurs) = p and P (all the three events occur simultaneously) = p2, where 0 < p < 1/2. Then the probability of at least one of the three events AB and C occurring is

Q7

Nine identical balls are numbers 1, 2,…9. Are put in a bag. A draws a ball and gets the number a. the ball is put back the beg. Next B draws a ball gets the number b. The probability that a and b satisfies the inequality a – 2b + 10 > 0 is

Q8

An unbiased die with faces marked 1, 2, 3, 4, 5 and 6 is rolled four times. Out of four face times. Out of four face values obtained, the probability that the minimum face value is not less than 2 and the maximum face value is not greater than 5 is then,

Q9

If the papers of 4 students can be checked by any one of the 7 teachers, then the probability that all the 4 papers are checked by exactly 2 teachers is

Q10

If m is a natural such that m ≤ 5, then the probability that the quadratic that the quadratic equation x2 + mx + has real roots is