Question

A dartboard has 10 equally sized slices numbered from 1 to 10. 

Some are grey and some are white. 

The slices numbered 1, 7, and 9 are grey. 

The slices numbered 2, 3, 4, 5, 6, 8, and 10 are 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 7 probability of X 

Let not X be the event that the dart lands on a slice that is not grey, 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 eve. Then, in the last column, enter the probability the event.

(b) Subtract. 1 - P(x) =

(c) Select the answer that makes the sentence true. 

Answer 1

(a) X = event that dart lands on grey slice

Not X = event that dart does not land on grey slice, meaning, it lands on white slice.

Now, the first row corresponds to event that dart lands on grey slice i.e. X, So check the outcomes 1,7 and 9 because they are the grey slices.

The second row corresponds to event that dart lands on white slice and not grey slices i.e. Not X . So, check the outcomes 2,3,4,5,6,8,10 because these are the white slices.

Now, the total number of slices are 10 i.e. 10 possible outcomes are there.

Probability = Number of favourable outcomes / Total number of outcomes

P(X) = Number of grey slices/ Total number of slices

P(Not X) = Number of grey slices/ Total number of slices

Event	Outcomes	Probability
X	1,7,9	P(X) = 3/10= 0.3
Not X	2,3,4,5,6,8,10	P(Not X) = 7/10= 0.7

(b)

1 - P(X) = 1 - 0.3 = 0.7

(c)

1 - P(X) is the same is P( Not X)