Question

For the following exercises, use the spinner shown in Figure 3 to find the probabilities indicated.

Landing on blue or a vowel

Answer 1

Consider the spinner provided in the exercise.

There are 8 sections in the spinner. Out of 8 sections, 2 sections are colored as blue.

 

If E is the event to landing on a blue, then the probability of event E will be,

P(E) = 2/8

Out of 8 sections, 4 sections are labeled by a vowel {A, E, I, O}.

 

If F is the event to landing on a vowel, then the probability of event F will be,

P(F) = 4/8

 

The blue sections in the spinner are labeled as ‘A’ and ‘D.’ That is, there is 1 blue section labeled by a vowel. So, the events E and F are not mutually exclusive events.

 

The probability of landing on a blue and a vowel will be,

P(E ∩ F) = 1/8

 

Use the formula for probability of the union of two events,

P(E ∪ F) = P(E) + P(F) – P(E ∩ F) ...... (1)

 

From formula (1) P(E ∪ F) = P(E) + P(F) – P(E ∩ F), the probability of landing on blue or a vowel will be,

P(E ∪ F) = 2/8 + 4/8 – 1/8

              = 5/8