What are my chances?

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 a b \frac{a}{b} , where a and b are positive coprime integers. Find a+b

Notes:

  1. This problem is not original
  2. Can somebody please post a solution for this


The answer is 31.

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1 solution

Sandeep Bhardwaj
Oct 13, 2014

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 ) = 0.75 + 0.65 0.85 = 0.55 = 11 20 \large \implies P(B and S)= 0.75 + 0.65 -0.85 = 0.55 =\frac{11}{20}

So as asked , the answer is 11 + 20 = 31 \large 11+20=\boxed{31}

Thanks Sandeep! This solution was very helpful!

Mark Mottian - 6 years, 8 months ago

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