a spinner has 5 equally sized sections, 2 of which are gray and 3 of which are blue. the spinner is spun…

a spinner has 5 equally sized sections, 2 of which are gray and 3 of which are blue. the spinner is spun twice. what is the probability that the first spin lands on blue and the second spin lands on gray? write your answer as a fraction in simplest form.

a spinner has 5 equally sized sections, 2 of which are gray and 3 of which are blue. the spinner is spun twice. what is the probability that the first spin lands on blue and the second spin lands on gray? write your answer as a fraction in simplest form.

Answer

Explanation:

Step1: Calculate probability of first - spin

The probability of landing on blue on the first spin is the number of blue sections divided by the total number of sections. There are 3 blue sections and 5 total sections. So the probability $P(\text{blue}_1)=\frac{3}{5}$.

Step2: Calculate probability of second - spin

The probability of landing on gray on the second spin is the number of gray sections divided by the total number of sections. There are 2 gray sections and 5 total sections. So the probability $P(\text{gray}_2)=\frac{2}{5}$.

Step3: Calculate combined probability

Since the two spins are independent events, the probability that the first spin lands on blue and the second spin lands on gray is the product of the probabilities of each event. So $P = P(\text{blue}_1)\times P(\text{gray}_2)=\frac{3}{5}\times\frac{2}{5}=\frac{6}{25}$.

Answer:

$\frac{6}{25}$