Mark takes both Science and Biology. Past results indicate that the probability of passing Biology is 0.75 and of failing Science is 0.35. The probability of passing at least one of the two subjects is 0.85. The probability that Mark will pass both subjects can be expressed as , where a and b are positive coprime integers. Find a+b
Notes:
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Let us assume
P(B)= Probability to pass Biology= 0.75 (given)
P(S)= Probability to pass Science=1-0.35(given) = 0.65
Given that P(B or S) = 0.85 (given)
P(B or S) = P(B) + P(S) - P(B and S)
⟹ P ( B a n d S ) = 0 . 7 5 + 0 . 6 5 − 0 . 8 5 = 0 . 5 5 = 2 0 1 1
So as asked , the answer is 1 1 + 2 0 = 3 1