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Updated on: 19 Jul 2025, 08:31
Originally posted by Sajjad1994 on 02 Jul 2025, 11:00.
Last edited by Sajjad1994 on 19 Jul 2025, 08:31, edited 2 times in total.
Last edited by Sajjad1994 on 19 Jul 2025, 08:31, edited 2 times in total.
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Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
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(N/A)
Question Stats:
33% (00:46) correct
66% (01:40) wrong based on 3 sessions
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A bag contains 5 red, 4 blue, and 8 orange jellybeans. 3 jellybeans are randomly selected from this bag.
| Quantity A | Quantity B |
| The probability of selecting a red, then a blue, then an orange jellybean | The probability of selecting a red, then another red, then an orange jellybean |
Updated on: 19 Jul 2025, 08:55
Originally posted by Sajjad1994 on 19 Jul 2025, 08:54.
Last edited by Sajjad1994 on 19 Jul 2025, 08:55, edited 1 time in total.
Last edited by Sajjad1994 on 19 Jul 2025, 08:55, edited 1 time in total.
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OE
Set up the probabilities in both quantities before calculating either value. The bag contains 5 red, 4 blue, and 8 orange jellybeans, and thus 17 total jellybeans.
In Quantity A, the probability of picking a red is \(\frac{5}{17}\). Once the red is selected, there are only 16 jellybeans left in the bag, so the probability of then picking a blue is \(\frac{4}{16}\), and then the probability of picking an orange is \(\frac{5}{18}\). Thus, Quantity A is equal to \(\frac{5}{17}*\frac{4}{16}*\frac{8}{15}\).
In Quantity B, the probability of picking a red first is still 5/17. Notice that once a red is picked first, there are now equal numbers of blues and reds left in the bag (4 each). Thus, the probability of now picking another red is 4/16 (equal to the probability in Quantity A of picking a blue at this point), and then the probability of picking an orange is still 8/15. Thus, Quantity B is also equal to \(\frac{5}{17}*\frac{4}{16}*\frac{8}{15}\).
The correct answer is (C): The two quantities are equal.
Set up the probabilities in both quantities before calculating either value. The bag contains 5 red, 4 blue, and 8 orange jellybeans, and thus 17 total jellybeans.
In Quantity A, the probability of picking a red is \(\frac{5}{17}\). Once the red is selected, there are only 16 jellybeans left in the bag, so the probability of then picking a blue is \(\frac{4}{16}\), and then the probability of picking an orange is \(\frac{5}{18}\). Thus, Quantity A is equal to \(\frac{5}{17}*\frac{4}{16}*\frac{8}{15}\).
In Quantity B, the probability of picking a red first is still 5/17. Notice that once a red is picked first, there are now equal numbers of blues and reds left in the bag (4 each). Thus, the probability of now picking another red is 4/16 (equal to the probability in Quantity A of picking a blue at this point), and then the probability of picking an orange is still 8/15. Thus, Quantity B is also equal to \(\frac{5}{17}*\frac{4}{16}*\frac{8}{15}\).
The correct answer is (C): The two quantities are equal.
