You are dealt one card from a 52 card deck. Then the card is replaced in the deck, the deck is shuffled, and you draw again. Find the probability of getting a picture card the first time and a club the second time. Express the probability as a simplified fraction.

There are 13 types of cards (A, 2, 3, 4, 5, 6, 7, 8, 9, 10, J, Q, K), out of which 3 (J, Q, K) are face cards. This means that the probability for the first half is 3/13. There are 4 suites (Club, Spade, Hearts, and Diamonds). This means the probability of attaining a club is 1/4. 3/13 * 1/4 = 3/52

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andromache andromache · Answer 2 · 2021-09-30T13:47:41+02:00

The probability of getting a picture card the first time and a club the second time is [tex]\frac{3}{52}[/tex].

Given that,

The card has 52 cards deck.
Also, the card does have 13 types of cards i.e. A, 2, 3, 4, 5, 6, 7, 8, 9, 10, J, Q, K). Out of these three cards i.e. J, Q, K are considered to be the face cards.

Based on the above information,

The probability of the first half should be [tex]\frac{3}{13}[/tex]

And, there are four types of suites i.e. Club, Spade, hearts & diamonds.

So, the probability of attaining the club is [tex]\frac{1}{4}[/tex]

Therefore the probability of getting a picture card is

[tex]= \frac{1}{4} \times \frac{3}{13} \\\\= \frac{3}{52}[/tex]

Thus we can conclude that the probability of getting a picture card the first time and a club the second time is [tex]\frac{3}{52}[/tex].

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