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`

Answer 1

`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`