Question

Hannah spins a spinner once and then randomly selects a marble from a bag. a representation of the spinner and the bag of marbles is shown below. a spinner with 6 equal sections labeled 1 through 6. 4 blue marbles, 2 red marbles, and 4 green marbles. she determines that the probability of spinning a multiple of 3 and randomly selecting a blue (b) marble is startfraction 2 over 15 endfraction. which best describes the accuracy of hannah’s answer? hannah’s answer is accurate. hannah’s answer is inaccurate. she may have correctly determined the probability of spinning a multiple of 3, but she considered the probability of randomly selecting a blue marble as one-fourth instead of startfraction 4 over 10 endfraction. hannah’s answer is inaccurate. she may have correctly determined the probability of randomly selecting a blue marble, but she considered the probability of spinning a multiple of 3 as startfraction 1 over 6 endfraction instead of startfraction 2 over 6 endfraction. hannah’s answer is inaccurate. the number of possible outcomes for the events is 60, not 15.

Answer 1

Hannah's calculation of the probability of spinning a multiple of 3 and selecting a blue marble as 2/15 is accurate based on the probabilities of individual events.

Step-by-step explanation:

The accuracy of Hannah's calculation for the probability of spinning a multiple of 3 and selecting a blue marble needs to be assessed based on two separate events. First, on the spinner labeled from 1 to 6, there are two multiples of 3: 3 and 6. Hence, the probability of spinning a multiple of 3 is 2 out of 6, which simplifies to 1 out of 3. Second, there are 4 blue marbles in a bag of 10 total marbles (4 blue, 2 red, 4 green). So, the probability of selecting a blue marble is 4 out of 10, which simplifies to 2 out of 5. To find the joint probability of both events occurring, we multiply their probabilities: (1/3) * (2/5) = 2/15. Therefore, Hannah's answer that the probability of spinning a multiple of 3 and randomly selecting a blue marble is 2/15 is indeed accurate.