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Question

In a lottery of $$50$$ tickets numbered $$1$$ to $$50$$, two tickets are drawn simultaneously. The probability that both the tickets drawn have prime numbers.


A
135
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B
1635
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C
735
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D
335
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Solution

The correct option is D $$\dfrac{3}{35}$$
Number of prime numbers between $$1$$ to $$50$$ is $$15$$
So probability of getting a prime number in the first draw will be $$=\dfrac{15}{50}$$
If one card is drawn from the pack of lottery tickets.
The number of prime numbers remaining in the bunch will be $$14$$
Total lottery tickets remaining in the bunch $$=49$$
The probability of getting a prime number $$\dfrac{14}{49}$$
So, the probability of getting prime numbers in two draws $$=\dfrac{15}{50}\times \dfrac{14}{49}=\dfrac{3}{35}$$

Maths

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