a spinner has 10 equally sized sections, 7 of which are gray and 3 of which are blue. the spinner is spun…

a spinner has 10 equally sized sections, 7 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 10 equally sized sections, 7 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

Answer:

$\frac{21}{100}$

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 10 total sections, so $P(\text{blue first})=\frac{3}{10}$.

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 7 gray sections and 10 total sections, so $P(\text{gray second})=\frac{7}{10}$.

Step3: Calculate combined probability

Since the two spins are independent events, the probability of the first spin landing on blue and the second spin landing on gray is the product of their individual probabilities. So $P = \frac{3}{10}\times\frac{7}{10}=\frac{21}{100}$.