a spinner is divided into 12 identical sectors and labeled 1 through 12. how many spins are expected for a…
a spinner is divided into 12 identical sectors and labeled 1 through 12. how many spins are expected for a multiple of 5 to be spun 8 times? select from the drop - down menu to correctly complete the sentence. the spinner is expected to have to spin approximately choose... times for a multiple of 5 has been spun 8 times.
Answer
Answer:
48
Explanation:
Step1: Identify multiples of 5
The multiples of 5 from 1 - 12 are 5 and 10. So 2 out of 12 sectors are multiples of 5.
Step2: Calculate probability
The probability $P$ of spinning a multiple of 5 is $P=\frac{2}{12}=\frac{1}{6}$.
Step3: Use expected - value formula
Let $n$ be the number of spins. We know that the expected number of times of getting a multiple of 5 is $E = n\times P$. We want $E = 8$. Substituting $E = 8$ and $P=\frac{1}{6}$ into the formula $E=n\times P$, we get $8=n\times\frac{1}{6}$.
Step4: Solve for $n$
To solve for $n$, we multiply both sides of the equation $8=n\times\frac{1}{6}$ by 6. So $n = 48$.