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Probability Part 1

Section: Mathematics

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Question : 33 of 100

Marks: +1, -0

Box I contains 30 cards numbered 1 to 30 and Box II contains 20 cards numbered 31 to

50.

A boxis selected at random and a card is drawn fromit. The number on the card is found to be anon-prime number. The probability that the cardwas drawn from Box I is :

[2 Sep 2020 Shift 1]

$\frac{8}{17}$
$\frac{2}{3}$
$\frac{4}{17}$
$\frac{2}{5}$

Solution:

Let

B_{1}

be the event where Box-I is selected.

\& B_{2} \rightarrow

where box-II selected

P(B_{1})=P(B_{2})=\frac{1}{2}

Let E be the event where selected card is nonprime.

For

B_1

: Prime numbers :

{2, 3, 5, 7, 11, 13, 17, 19, 23, 29}

For

B_2

: Prime numbers :

{31, 37, 41, 43, 47}

P(E)=P(B_{1})\times P\left(\frac{E}{B_{1}}\right)

+P(B_{2})P\left(\frac{E}{B_{2}}\right)

=\frac{1}{2}\times\frac{20}{30}+\frac{1}{2}\times\frac{15}{20}

Required probability :

P\left(\frac{B_{1}}{E}\right)=\frac{\frac{1}{2}\times\frac{20}{30}}{\frac{1}{2}\times\frac{20}{30}+\frac{1}{2}\times\frac{15}{20}}

=\frac{\frac{2}{3}}{\frac{2}{3}+\frac{3}{4}}=\frac{8}{17}

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