SOLUTION: in an exam only 20% failed in maths and 15% failed in chemistry and 10% failed in both maths and chemistry. determine probability student selected in random has passed maths and ch

Question 909941: in an exam only 20% failed in maths and 15% failed in chemistry and 10% failed in both maths and chemistry. determine probability student selected in random has passed maths and chemistry
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
20% failed math
15% failed chemistry
10% failed both.

p(a or b) = p(a) + p(b0 - p(ab)

in this problem, this becomes:

p(fail math or chem) = p(fail math) + p(fail chem) - p(fail both math and chem).

that becomes:

p(fail math or chem) = .20 + .15 - .10 = .25

this mean that 25% failed math or chem or both.

that means that 75% didn't fail either one which means that they passed both.

that's your solution.

i also looked at it another way.

if 10% failed both, that means that 90% passed one or the other or both.

p(a or b) = p(a) + p(b) - p(ab).

that becomes:

p(pass math or chem or both) = p(pass math) + p(pass chem) - p(pass math and chem).

we know that p(pass math or chem or both) = 90%.

we know that p(pass math) = 80%

we know that p(pass chem) = 85%)

we get:

p(pass math or chem or both) = p(pass math) + p(pass chem) - p(pass math and chem) becomes:

90% = 80% + 85% - p(pass math and chem).

solve for p(pass math and chem) and you get:

p(pass math and chem) = 80% + 85% - 90% = 165% - 90% = 75%.

looks good either way so I'll go with that.

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