Question

she determines that the probability of spinning a multiple of 3 and randomly selecting a blue (b) marble is $\frac{2}{15}$. which best describes the accuracy of hannahs answer? hannahs answer is accurate. hannahs 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 $\frac{1}{4}$ instead of $\frac{4}{10}$. hannahs 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 $\frac{1}{6}$ instead of $\frac{2}{6}$. hannahs answer is inaccurate. the number of possible outcomes for the events is 60, not 15.

Explanation:

Step1: Assume number of outcomes for spinning

Let's assume there are 6 outcomes for spinning (not given in full - but a common spinner number of sections). Multiples of 3 among 6 possible outcomes are 3 and 6, so probability of spinning a multiple of 3 is $\frac{2}{6}=\frac{1}{3}$.

Step2: Assume number of marbles

Assume there are 10 marbles in total with 4 blue marbles. So probability of selecting a blue marble is $\frac{4}{10}=\frac{2}{5}$.

Step3: Calculate combined probability

The probability of two independent events A and B occurring is $P(A)\times P(B)$. So the probability of spinning a multiple of 3 and selecting a blue marble is $\frac{1}{3}\times\frac{2}{5}=\frac{2}{15}$.

Answer:

Hannah's answer is accurate.