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.

Answer 1

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`