Question

a wheel has 5 equally sized slices numbered from 1 to 5.
some are grey and some are white.
the slice numbered 1 is grey.
the slices numbered 2, 3, 4, and 5 are white.
the wheel is spun and stops on a slice at random.
let x be the event that the wheel stops on a white slice, and let
p(x) be the
probability of x.
let not x be the event that the wheel stops on a slice that is not white, and let
p(not x) be the probability of not x.
(a) for each event in the table, check the outcome(s) that are contained in the event. then, in the last column, enter the probability of the event.
(b) subtract.
1 - p(not x) =

Explanation:

Step1: Determine the probability of \(X\)

Since there are 4 white - colored slices (slices numbered 2, 3, 4, 5) out of 5 total slices.
The probability formula is \(P(X)=\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}\).
So, \(P(X)=\frac{4}{5}\)

Step2: Determine the probability of \(not - X\)

We know that \(P(not - X)=1 - P(X)\)
Substitute \(P(X)=\frac{4}{5}\) into the formula: \(P(not - X)=1-\frac{4}{5}=\frac{1}{5}\)

Step3: Verify \(1 - P(not - X)\)

Substitute \(P(not - X)=\frac{1}{5}\) into \(1 - P(not - X)\)
\(1-\frac{1}{5}=\frac{4}{5}\)

Answer:

(a) For event \(X\): \(P(X)=\frac{4}{5}\), for event \(not - X\): \(P(not - X)=\frac{1}{5}\) (Outcomes for \(X\): 2, 3, 4, 5; Outcomes for \(not - X\): 1)
(b) \(1 - P(not - X)=\frac{4}{5}\)