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Question
Select the correct option from the given alternatives :
There are 2 shelves. One shelf has 5 Physics and 3 Biology books and the other has 4 Physics and 2 Biology books. The probability of drawing a Physics book is
Options
`9/14`
`31/48`
`9/38`
`1/2`
Solution
`31/48`
Explanation:
Let event S1: First shelve is selected.
event S2: Second shelve is selected.
event P: Drawing a physics book.
∴ P(S1) = `1/2` and P(S2) = `1/2`
First shelve has 5 physics and 3 biology books, i.e., total of 8 books.
∴ `"P"("P"/"S"_1) = (""^5"C"_1)/(""^8"C"_1) = 5/8`
Similarly, `"P"("P"/"S"_2) = (""^4"C"_1)/(""^6"C"_1) = 4/6 = 2/3`
∴ P(P) = `"P"("S"_1)*"P"("P"/"S"_1) + "P"("S"_2)*"P"("P"/"S"_2)`
= `1/2 xx 5/8 + 1/2 xx 2/3`
= `31/48`
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