Question

Suppose that two cards are drawn at random x from a deck of cards. Let x be the number of aces obtained. Then value of E(x) is

विकल्प

• `37/221`

• `27/221`

• `1/13`

• `2/13`

Answer 1

`2/13`

Explanation:

(i) When two cards are drawn let no ace occurs.

Two non-ace cards may be drawn in 48C₂ ways = `(48 xx 47)/2 = 24 xx 47` = 1128

Out of 52 any two cards may be drawn in 5C₂ = `(52 xx 51)/2 = 26 xx 51` = 1326 ways

∴ Probability of getting no ace = `1128/1326` ways

(ii) One ace and one non-ace cards may be drawn in 4C₁ × 48C₁ = 4 × 48 = 192 ways.

∴ Probability of getting one ace and one non-ace card = `192/1326`

(iii) The number of ways. of drawing two aces = 4C₂ = 6

∴ Probability of getting 2 aces = `6/1326` 

∴ Probability distribution is

X	0	1	2
P(x)	`1128/1326`	`192/1326`	`6/1326`

∴ E(x) = `sumP_1X_1 = 1128/1326 xx 0 + 1 xx 192/1326 + 2 xx 6/1326`

= `192/1326 + 12/1326`

= `204/1326`

= `2/13`