SATHEE: Probability 3 Question 33

Probability 3 Question 33

33. A box contains 100 tickets numbered $1, 2, \dots, 100$ . 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

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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

$\begin{aligned} ∴ \begin{aligned} P (A \cap B) & = \frac{^{5} C_{1}}{^{100} C_{2}} \\ and P (A) & = \frac{^{10} C_{2}}{^{100} C_{2}} \\ Then P \frac{B}{A} & = \frac{P (A \cap B)}{P (A)} \\ = \frac{^{5} C_{1}}{^{10} C_{2}} = \frac{1}{9} \end{aligned} \end{aligned}$

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Probability 3 Question 33

33. A box contains 100 tickets numbered 1,2,…,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… .

Analytical and Descriptive Questions

Solution:

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33. A box contains 100 tickets numbered $1, 2, \dots, 100$ . 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… .