Question

a dartboard has 8 equally sized slices numbered from 1 to 8.
some are grey and some are white.
the slices numbered 1, 2, 3, 4, 6, 7, and 8 are grey.
the slice numbered 5 is white.
a dart is tossed and lands on a slice at random.
let ( x ) be the event that the dart lands on a grey slice, and let ( p(x) ) be the
probability of ( x ).
let not ( x ) be the event that the dart lands on a slice that is not grey, and let
( p(\text{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(x)=square )

Explanation:

Step1: Calculate \( P(X) \)

The formula for probability is \( P=\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} \).
The total number of slices \( n = 8 \).
The number of grey - slices (favorable outcomes for event \( X \)) \( m=7 \).
So, \( P(X)=\frac{7}{8} \).

Step2: Calculate \( P(\text{not }X) \)

The number of non - grey slices (favorable outcomes for event \(\text{not }X\)) \( k = 1 \).
Using the probability formula \( P=\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} \), we get \( P(\text{not }X)=\frac{1}{8} \).

Step3: Calculate \( 1 - P(X) \)

Substitute \( P(X)=\frac{7}{8} \) into \( 1 - P(X) \).
\( 1-\frac{7}{8}=\frac{8 - 7}{8}=\frac{1}{8} \).

Answer:

• \( P(X)=\frac{7}{8} \), and for event \( X \), the checked outcomes are \( 1\), \(2\), \(3\), \(4\), \(6\), \(7\), \(8\).
• \( P(\text{not }X)=\frac{1}{8} \), and for event \(\text{not }X\), the checked outcome is \(5\).
• \( 1 - P(X)=\frac{1}{8} \)