Question

The probability of the spinner landing on the shaded part is p=1/3. The probability of it landing on an unshaded part is q=2/3 times. If you spin the spinner n = 3 times, what is the probability of it landing on the shaded part r = 2 times? Use the equation P(r) = nCr pr qn−r, where

Answer 1

Answer:

The correct answer is 0.5.

Step-by-step explanation:

The probability of a spinner landing on the shaded part follows binomial distribution.

Equation to be used is P(r) = $\left[\begin{array}{ccc}n\\r\end{array}\right]$  × $p^{r}$ × $q^{n-r}$ , where n is the number of times the spinner is spun and r is the number of times the spinner falls on the shaded region.

The probability of the spinner landing on the shaded part is p = $\frac{1}{3}$. The probability of it landing on the unshaded part is q = $\frac{2}{3}$.

The spinner is spun n = 3 times.

We need to find the probability of it landing on the shaded part r = 2.

∴ Putting the values in the equation gives,

P(r) = $\left[\begin{array}{ccc}3\\2\end{array}\right]$  × $\frac{1}{2} ^{2}$ × $\frac{2}{3} ^{1}$ = 3 × $\frac{2}{3}$ × $\frac{1}{4}$ = 0.5