A problem in Mathematics is given to three students A,B,C whose chance of solving it are 1/2, 3/4 and V4 respectively. If all three students attempt the problem then the probability that the problem get solved is
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Answer:
Probability that A is able to solve = P(A) = (1 / 2).
Probability that B is able to solve = P(B) = (3 / 4).
Probability that C is able to solve = P(C) = (1 / 4).
Probability that A is not able to solve = P(a) = 1 – P(A) = (1 / 2).
Probability that B is not able to solve = P(b) = (1 / 4).
Probability that C is not able to solve = P(c) = (3 / 4).
When A, B and C are independent events; the probability that none of them will be able to solve if all of them try independently = P(a)*P(b)*P(c) = (1 / 2)*(1 / 4)*(3 / 4) = (3 / 32).
Therefore, the probability that the problem will be solved if all of them try independently = 1 – P(a)*P(b)*P(c) = (29 / 32).
Answer:
Probability that A is able to solve = P(A) = (1 / 2).
Probability that B is able to solve = P(B) = (3 / 4).
Probability that C is able to solve = P(C) = (1 / 4).
Probability that A is not able to solve = P(a) = 1 – P(A) = (1 / 2).
Probability that B is not able to solve = P(b) = (1 / 4).
Probability that C is not able to solve = P(c) = (3 / 4).
When A, B and C are independent events; the probability that none of them will be able to solve if all of them try independently = P(a)*P(b)*P(c) = (1 / 2)*(1 / 4)*(3 / 4) = (3 / 32).
Therefore, the probability that the problem will be solved if all of them try independently = 1 – P(a)*P(b)*P(c) = (29 / 32).