Probability 3 Question 33
33. 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… .
$(1985,2 M)$
Analytical and Descriptive Questions
Show Answer
Solution:
- 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
$$ \begin{aligned} & \therefore \quad \begin{aligned} P(A \cap B) & =\frac{{ }^{5} C _1}{{ }^{100} C _2} \\ \text { and } \quad P(A) & =\frac{{ }^{10} C _2}{{ }^{100} C _2} \\ \text { Then } \quad P \frac{B}{A} & =\frac{P(A \cap B)}{P(A)} \\ & =\frac{{ }^{5} C _1}{{ }^{10} C _2}=\frac{1}{9} \end{aligned} \end{aligned} $$
