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

The correct answer is 0.5.

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 =
`(1)/(3)`. The probability of it landing on the unshaded part is q =
`(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]` ×
`(1)/(2) ^(2)` ×
`(2)/(3) ^(1)` = 3 ×
`(2)/(3)` ×
`(1)/(4)` = 0.5