Question

Two digit numbers are formed using the digits 0, 1, 2, 3, 4, 5 where digits are not repeated.

P is the event that the number so formed is even.
Q is the event that the number so formed is greater than 50.
R is the event that the number so formed is divisible by 3.
Then write the sample space S and events P, Q, R using set notation.

Answer 1

As we have to form two-digit numbers, 0 cannot be at the tens place.
The sample space is
S = {10, 12, 13, 14, 15, 20, 21, 23, 24, 25, 30, 31, 32, 34, 35, 40, 41,
42, 43, 45, 50, 51, 52, 53, 54}
Let P be the event that the number formed is an even number.
∴ P = {10, 12, 14, 20, 24, 30, 32, 34, 40, 42, 50, 52, 54}
Let Q be the event that the number formed is greater than 50.
∴ Q = {51, 52, 53, 54}
Let R be the event that the number formed is divisible by 3.
∴ R = {12, 15, 21, 24, 30, 42, 45, 51, 54}