SOLUTION: Please answer this question .., probability that a student A can solve a certain problem is 3/4 and that another student B can solve it is 4/5. If both try independently , what is

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Question 1072401: Please answer this question .., probability that a student A can solve a certain problem is 3/4 and that another student B can solve it is 4/5. If both try independently , what is the probability that i) The problem is solved ? ii) The problem is not solved?
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
p(A) = 3/4

p(B) = 4/5

since these are independent events, .....

p(A and B) = p(A) * p(B) = 3/4 * 4/5 = 12/20 = 3/5.

p(A or B) = p(A) + p(B) - p(A and B)

p(A or B) is the probability that the problem is solved, since either A solves it or B solves it or both A and B solve it at the same time.

p(A or B) = p(A) + p(B) - p(A and B) becomes:

p(A or B) = 3/4 + 4/5 - 3/5.

put everything under the same common denominator and you get:

p(A or B) = 15/20 + 16/20 - 12/20

combine like terms under the same denominator and you get:

p(A or B) = (15 + 16 - 12) / 20

combine like terms to get:

p(A or B) = 19 / 20.

that's the probability that the problem will be solved.

the probability that the problem will not be solved is 1 - 19/20 = 1/20.

in the formula of p(A or B) = p(A) + p(B) - p(A and B), p(A and B) is assumed to be part of p(A) and part of p(B) which means they are being double counted.

the subtraction of p(A and B) therefore eliminates the double counting.