Question

.Four digit number's are formed by using the digits 1,2,3,4,5 without repeating any digit. Find the probability that a
number chosen at random is an odd number.
​

Answer 1

Answer:

a

Given digits are 1, 2, 3, 4.

Possibilities for units place digit (either 1 or 3) = 2

Let S be the sample space i.e set of all numbers formed by the digits 1,2,3,4(without repetition).

Let A be an event of getting odd numbers.

If 1 comes at unit's place, then no. of ways of forming odd number is 3!.

Similarly, if digit 3 appears at unit's place then there are 3! ways of arranging remaining 3 digits i.e. 1,2, and 4 to form odd number.

∴ There will be 3!+3!=6+6=12 odd numbers which are formed by the digits 1,2,3 and 4.

⟹n(A)=12

Number of numbers formed by 1, 2, 3, 4 (without repetitions) =4!=24=n(S)

∴ P(A)=

n(S)

n(A)

∴ Required probability = 24/12 =1/2