A student is tasked with selecting two cards with replacement from a fair poker
ID: 3038647 • Letter: A
Question
A student is tasked with selecting two cards with replacement from a fair poker deck of 52 cards. Which two demonstrate correct student reasoning about possible results of this experiment? Choose 2 answers "Getting two kings is just as likely as getting two 10s." "If you get a red card on the first pull, you're more likely to get a black card on the second pull." "The outcome of red king on first pull and black two on second pull is just as likely as getting the same ace on both pulls." "Since there are 52 cards in the deck, there's an 8 in 104 chance that I get 5 on both draws." "With two draws, there is a 1 in 3 chance of getting a red card both times: the three possible outcomes are two red two black, and one red and one black."Explanation / Answer
The probability of getting a 10 on the 1st draw is 4/52. After replacement, the probability of getting a 10 again on the 2nd draw is also 4/52 (as there are 4 10s in a deck of 52 cards). Therefore, the probability of getting a 10 on both the 1st and the 2nd draws is 4/52*4/52 = 1/169.This is, thus a correct statement.
2. The probability of getting a red card on the 1st draw is 26/52. After replacement, the probability of getting a red card again on the 2nd draw is also 26/52(as there are 26 red cards in a deck of 52 cards). Therefore, the probability of getting a red card on both the 1st and the 2nd draws is 26/52*26/52 = 1/4.
The probability of getting a red card on the 1st draw is 26/52. After replacement, the probability of getting a black card on the 2nd draw is also 26/52. Therefore, the probability of getting a red card on the 1st and a black card on the 2nd draws is 26/52*26/52 = 1/4. The statement is incorrect.
3. The probability of getting a red king on the 1st draw is 2/52. After replacement, the probability of getting a black 2 on the 2nd draw is also 2/52(as there are 2red kings and 2 black 2s in a deck of 52 cards). Therefore, the probability of getting a red king on the 1st draw and a black 2 on the 2nd draw is 2/52*2/52 =1/676.
The probability of getting an ace on the 1st draw is 4/52 (as there are 4 aces in a deck of 52 cards). After replacement, the probability of getting the same ace on the 2nd draw is 1/52. Therefore, the probability of getting the same ace on the 1st and the 2nd draws is 4/52 *1/52 = 1/676. This is, thus a correct statement.
4. The probability of getting a 5 on the 1st draw is 4/52. After replacement, the probability of getting a 5 again on the 2nd draw is 4/52 (as there are 4 5s in a deck of 52 cards). Therefore, the probability of getting a 5 on both the 1st and the 2nd draws is 4/52*4/52 = 1/169. The statement is incorrect.
5. The probability of getting a red card on the 1st draw is 26/52. After replacement, the probability of getting a red card again on the 2nd draw is also 26/52(as there are 26 red cards in a deck of 52 cards). Therefore, the probability of getting a red card on both the 1st and the 2nd draws is 26/52*26/52 = 1/4. The statement is incorrect.
Thus, the 1st and the 3rs statements are the only 2 correct statements.
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