probability of solving specific problem independently by A,B,C are 1/2,1/3,1/4. If they all try the problem independently,find the probability that problem is solved.
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Step-by-step explanation:
Given Probability of solving specific problem independently by A,B,C are 1/2,1/3,1/4. If they all try the problem independently, find the probability that problem is solved.
- Probability that A will be able to solve the problem will be P(A) = 1/2
- Probability that B will be able to solve the problem will be P(B) = 1/3
- Probability that C will be able to solve the problem will be P(C) = 1/4
- Probability that A will not be able to solve the problem will be P (a) = 1 – P (A)
- = 1 – 1/2
- = 1/ 2
- Probability that B will not be able to solve the problem will be P (b) = 1 – P (B)
- = 1 – 1/3
- = 2/3
- Probability that C will not be able to solve the problem will be P (c) = 1 – P (C)
- = 1 – 1/4
- = 1/4
- Now A,B,C are independent, the probability that none of them will be able to solve if all of them try independently will be P(a) x P(b) x P(c)
- = 1/2 x 2/3 x 1/4
- = 2 / 24
- = 1 / 12
- Therefore the probability that the problem will be solved will be
- = 1 – P(a) x P(b) x P(c)
- = 1 – 1/12
- = 11/12
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Step-by-step explanation:
The probability that A can solve a problem in Statistics is 4/5, that B can solve it is 2/7, that C can solve it is 4/9. If all them try independently, find the probability that the problem will be solved.
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