Question

Two cards are drawn simultaneously from a well shuffled pack of 52 cards. Draw the probability distribution table of the number of aces.​

Answer 1

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step-by-step explanation:

let X be the random variable.

then,

X denotes the number of aces in a draw of 2 cards.

therefore,

X can assume the value 0,1 or 2.

No. of ways of drawing 2 cards out of 52

= C(52,2).

now,

P(X =0) =P(both non-aces i.e, 2 non-aces out of 48)

= C(48,2)/C(52,2)

= 48×47×2/2×52×51

= 188/221

now,

P(X=1)= P{(1 ace out of 4) and (1 ace out of 48)}

= C(4,1)×C(48,1)/C(52,2)

= 4×48×2/52×51

= 32/221

again,

P(X=2) = P(both aces)

= C(4,2)/C(52,2)

= 4×3×2/2×52×51

= 1/221

Now,

the probability distribution table is drawn

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Kindly refer to the attachment ✍️✍️

Answer 2

step-by-step explanation:

let X be the random variable.

then,

X denotes the number of aces in a draw of 2 cards.

therefore,

X can assume the value 0,1 or 2.

No. of ways of drawing 2 cards out of 52

= C(52,2).

now,

P(X =0) =P(both non-aces i.e, 2 non-aces out of 48)

= C(48,2)/C(52,2)

= 48×47×2/2×52×51

= 188/221

now,

P(X=1)= P{(1 ace out of 4) and (1 ace out of 48)}

= C(4,1)×C(48,1)/C(52,2)

= 4×48×2/52×51

= 32/221

again,

P(X=2) = P(both aces)

= C(4,2)/C(52,2)

= 4×3×2/2×52×51

= 1/221

Now,

the probability distribution table is drawn