The probability of solving a problem by three students X,Y,Z are 1/4,3/7and 2/9 respectively. if all of them try independently then the probability that the problem could not be solved is a)1/3 b)1/4 c)1/5 d) 2/5 e) 3/7

Question

Ans given is 3/7.
Mine is 1/3.
Approach: P(~X)P(~Y)P(~Z)=  3/4 * 4/7 * 7/9 = 1/3

Comments

"problem could not be solved by any?"
If so your answer is right.

---

Ans if the question is that all of them try to solve the problem together  and the problem couldn't not be solved by all three of them then it should be   1-  {P(A). P(B). P(C) is it correct sir??

Answer 1

Sahil, your answer is right.

Answer 2

The probability that the problem is not solved by any of the students is the product of the probabilities that each student fails to solve the problem. So we have:

P(problem not solved) = P(X fails) * P(Y fails) * P(Z fails)

P(X solves the problem) = 1/4 P(X fails to solve the problem) = 1 - P(X solves the problem) = 3/4 P(Y solves the problem) = 3/7 P(Y fails to solve the problem) = 1 - P(Y solves the problem) = 4/7 P(Z solves the problem) = 2/9 P(Z fails to solve the problem) = 1 - P(Z solves the problem) = 7/9

So we have:

P(problem not solved) = (3/4) * (4/7) * (7/9) = 1/3

Therefore, the probability that the problem could not be solved is 1/3. Answer: (a)

 

Answer 3

(1-1/4)(1-3/7)(1-2/9)

(3/4) * (4/7) *(7/9)

1/3 will be answer

Answer 4

1/3 is the correct Answer