Question

Two numbers are selected from first six even natural numbers at random without replacement. If X denotes the greater of two numbers selected, find the probability distribution of X.

Answer 1

The two even natural numbers can be selected from the first six even natural numbers without replacement in 6 × 5 = 30 ways.

X represent the greater of two numbers.

Therefore, X can take the values 4, 6, 8, 10, 12.

For X = 4: Possible observations are (2, 4), (4, 2).

∴ P(X = 4) = `2/30 = 1/15`

For (X = 6): Possible observations are

(2, 6), (6, 2), (4, 6), (6, 4)

P(X = 6) = `4/30 = 2/15`

For X = 8: Possible observations are

(2, 8), (8, 2), (4, 8), (8, 4), (6, 8), (8, 6)

P(X = 8) = `6/30 = 1/5`

For X = 10: Possible observations are

(2, 10), (10, 2), (4, 10), (10, 4), (6, 10), (10, 6), (8, 10), (10, 8)

P(X = 10) = `8/30 = 4/15`

For X = 12: Possible observations are

(2, 12), (12, 2), (4, 12), (12, 4), (6, 12), (12, 6), (8, 12), (12, 8), (10, 12), (12, 10)

P(X = 12) = `10/30 = 1/3`

Therefore, the probability distribution

X	4	6	8	10	12
P(X)	`1/15`	`2/15`	`1/5`	`4/15`	`1/3`