Probability Ques 73
A box contains $100$ tickets numbered $1,2, \ldots, 100$. Two tickets are chosen at random. It is given that the maximum number on the two chosen tickets is not more than $10$. The maximum number on them is $5$ with probability… .
$(1985,2\ M)$
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Answer:
Correct Answer: 73.$(\frac{1}{9})$
Solution:
Formula:
Set theoretical notation of probability and some important results:
- Let $A$ be the event that the maximum number on the two chosen tickets is not more than $10$ , and $B$ be the event that the minimum number on them is $5$
$ \begin{aligned} & \therefore \quad \begin{aligned} P(A \cap B) & =\frac{{ }^{5} C _{1}}{{ }^{100} C _{2}} \\ \text { and } \quad P(A) & =\frac{{ }^{10} C _2}{{ }^{100} C _2} \\ \text { Then } \quad P (\frac{B}{A}) & =\frac{P(A \cap B)}{P(A)} \\ & =\frac{{ }^{5} C _1}{{ }^{10} C _2}=\frac{1}{9} \end{aligned} \end{aligned} $
BETA
