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Question
Using the digits 0, 2, 3, 5 the two-digit numbers are constructed without repetition of digits. Find the probability of the following events:
Condition for event B: The number formed is prime number.
Solution
As we have to form two-digit numbers, 0 cannot be at tens place.
The Sample Space S = {20, 23, 25, 30, 32, 35, 50, 52, 53}
∴ n (S) = 9
Let B be the event that the number formed is prime.
Prime two-digit numbers= {23, 53}
⇒ n(B) = 2
Thus, P(B) = `"Number of prime digits numbers"/"Total number of two-digits numbers"`
= `2/9`
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