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$A spinner has 5 equally sized sections, 1 of which is gray and 4 of which are blue. The spinner is spun twice. What is the probability that the first spin lands on blue and the second spin lands on gray? Write your answer as a fraction in simplest form.$

A spinner has $5$ equally sized sections, $1$ of which is gray and $4$ 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? $\newline$ Write your answer as a fraction in simplest form.

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Probability of independent and dependent events

Full solution

Q. A spinner has

5

equally sized sections,

1

of which is gray and

4

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?

\newline

Write your answer as a fraction in simplest form.

Calculate Probability of First Spin: First spin lands on blue: There are $4$ blue sections out of $5$ total sections. $\newline$ Probability of first spin landing on blue $= \frac{4}{5}$ .
Calculate Probability of Second Spin: Second spin lands on gray: There is $1$ gray section out of $5$ total sections. $\newline$ Probability of second spin landing on gray $= \frac{1}{5}$ .
Calculate Combined Probability: Calculate the combined probability of both events happening in sequence. $\newline$ Combined probability = Probability of first spin landing on blue $\times$ Probability of second spin landing on gray. $\newline$ Combined probability = $(\frac{4}{5}) \times (\frac{1}{5})$ .
Perform Multiplication: Perform the multiplication to find the combined probability. $\newline$ Combined probability = $\frac{4}{25}.$

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