From a pack of 52 cards, two cards are drawn in succession one by one without replacement. The probability that both are aces is...

Urijah Lawrence

Urijah Lawrence

Answered question

2023-03-13

From a pack of 52 cards, two cards are drawn in succession one by one without replacement. The probability that both are aces is...

Answer & Explanation

laminimpfv

laminimpfv

Beginner2023-03-14Added 3 answers

There are 52 cards in a pack of cards.
There are 4 aces in that pack.
Event of choosing one card n(S)=C152
Event of choosing an ace n(A1)=C14
If one card is drawn at random, then the probability of getting an ace is P(A1)
n(A1)n(S)=C14C152 P(A)=n(A)n(S)
=452=113
There are 51 cards in that pack.
There are 3 aces in that pack.
Event of choosing one card n(S)=C151
Event of choosing a second ace n(A2)=C13
If one card is drawn at random, then the probability of getting a second ace without any replacement is P(A2)
n(A2)n(S)=C13C151 (one card is drawn at random)
=351=117
The odds of receiving two aces without any replacement are calculated by calculating the odds of getting an ace and a second ace without any replacement.
P(A1)×P(A2)=113×117=1221

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