A student is tasked with selecting two cards with replacement from a fair poker
ID: 3038233 • 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? "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 l 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
A fair deck of cards has 26 each of red and black cards. There are 4 Kings ( 2 red, 2 black) and 4 Aces ( 2 red and 2 black). Similarly, there are 4 cards ( 2 red and 2 black) representing each of the numbers ranging from 1 to 10.
1.Getting 2 kings is as likely as getting 2 10s is a correct statement. The probabilities of getting a king in the 1st and the 2nd draws are 4/52 and 3/51 respectively so that the probabilty of getting 2 kings in 2 draws is (4/52)*(3/51) = 12/2652. This is same as the probabilty of getting 2 10s in 2 draws. The statement is correct.
2. The probability of getting a red card on the 1st pull is 26/52 = ½. The probabilities of getting a red or a black card on the 2nd pull are 25/51 and 26/51 respectively so that the probability of getting a black card on the 2nd pull is hihjer than the the probability of getting a red card on the 2nd pull. The statement is correct.
3. The probability of getting a red king on the 1st pull is 2/52 = 1/26. The probability of getting a black 2 on the 2nd pull is 2/51 . Therefore, The probability of getting a red king on the 1st pull and black 2 on the 2nd pull is (1/26)*(2/51) = 2/1326 = 1/663. Same ace cannot be pulled twice, but if the intention is an ace of the same color, then the probability of getting an ace of a paricular color in the 1st pull is 2/52 = 1/26. The probability of getting an ace of the same color in the 2nd pull is 1/51 so that the probability of getting an ace of a paricular color in the 1st pull and an ace of the same color in the 2nd pull is (1/26)*(1/51) =1/ 1326. The statement is incorrect.
4. The probability of getting a 5 in the 1st draw is 4/52 = 1/13. The probability of getting a 5 on the 2nd draw is 3/51 = 1/17 so that the probability of getting a 5 in the 1st draw and also in the 2nd draw is (1/13)*(1/17) = 1/221 8/104. The statement is incorrect.
5. With the 1st draw, the probability of getting a red card is 26/52 = ½. The probability of getting a red card on the 2nd draw is 25/51 so that the the probability of getting a red card on both the 1st and the 2nd draws is (1/2)*(25/51) = 25/102 1/3. The statement is incorrect.
The 1st and the 2nd students demonstrate correct reasoning about possible results of the experiment.
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