Probability of solving specific problem independently by A and B are
1/2 and 1/3 respectively. If both try to solve the problem independently, find the probability that the problem is solved?
1/3
2/3
4/5
5/6
1
solve it
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- DanaJ
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First off, let's remember that the probability of something NOT happening is 1 - (the probability of that event happening).
Three cases in which the problem gets solved:
1. they both get it at the same time. P = 1/3 * 1/2 = 1/6
2. A gets it, but B does not. P = 1/2 * (1 - 1/3) = 1/2 * 2/3 = 1/3
3. A doesn't get it, but B does. P = (1 - 1/2)*1/3 = 1/2*1/3 = 1/6
Sum of P = 1/6 + 1/6 + 1/3 = 2/6 + 1/3 = 1/3 + 1/3 = 2/3.
Side note: another way of doing this is by noticing that the probability of the problem being solved is 1 - the probability of the event that the problem is not solved by either.
P' = (1 - 1/2)*(1 - 1/3) = 1/2 * 2/3 = 1/3
1 - P' = 1 - 1/3 = 2/3.
Three cases in which the problem gets solved:
1. they both get it at the same time. P = 1/3 * 1/2 = 1/6
2. A gets it, but B does not. P = 1/2 * (1 - 1/3) = 1/2 * 2/3 = 1/3
3. A doesn't get it, but B does. P = (1 - 1/2)*1/3 = 1/2*1/3 = 1/6
Sum of P = 1/6 + 1/6 + 1/3 = 2/6 + 1/3 = 1/3 + 1/3 = 2/3.
Side note: another way of doing this is by noticing that the probability of the problem being solved is 1 - the probability of the event that the problem is not solved by either.
P' = (1 - 1/2)*(1 - 1/3) = 1/2 * 2/3 = 1/3
1 - P' = 1 - 1/3 = 2/3.