Probability Problem Involving Spinner
I can see that the image contains a question about a probability problem involving a spinner. The problem states that the spinner is divided into equally sized sections, 3 of which are gray and 5 of which are blue. The question asks for the probability that the first spin lands on gray and the second spin lands on blue.
To solve this, we need to calculate the probability of both events happening one after the other. The chance that the first spin lands on gray is 3 out of 8, as there are 3 gray sections out of a total of 8. The probability of a specific event is calculated by the formula:
\[ P(\text{Event}) = \frac{\text{number of favorable outcomes}}{\text{total number of possible outcomes}} \]
For the first spin:
\[ P(\text{first spin on gray}) = \frac{3}{8} \]
For the second spin, the probability that the spin lands on blue is 5 out of 8, as there are 5 blue sections.
For the second spin:
\[ P(\text{second spin on blue}) = \frac{5}{8} \]
Since these are independent events, the overall probability of both occurring in sequence is the product of the two individual probabilities:
\[ P(\text{gray then blue}) = P(\text{first spin on gray}) \times P(\text{second spin on blue}) \]
\[ P(\text{gray then blue}) = \left( \frac{3}{8} \right) \times \left( \frac{5}{8} \right) \]
\[ P(\text{gray then blue}) = \frac{3 \times 5}{8 \times 8} \]
\[ P(\text{gray then blue}) = \frac{15}{64} \]
So, the probability that the first spin lands on gray and the second spin lands on blue is \(\frac{15}{64}\).
