Question

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

Not landing on yellow or a consonant

Answer 1

Consider the spinner provided in the exercise.

 

There are 8 sections in the spinner. Out of 8 sections, 1 section is colored as yellow.

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

P(E) = 1/8

 

Out of 8 sections, 4 sections are labeled by a consonant {B, D, C, F}.

 

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

P(F) = 4/8

 

The yellow section in the spinner is labeled as ‘O,’ not a consonant. So, the events E and F are mutually exclusive events.

 

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

P(E ∪ F) = P(E) + P(F) ...... (1)

 

From formula (1) P(E ∪ F) = P(E) + P(F), the probability of landing on yellow or a consonant will be,

P(E ∪ F) = 1/8 + 4/8

              = 5/8

 

Use the complement law for probability,

P(E\') = 1 – P(E) ...... (2)

 

From formula (2) P(E\') = 1 – P(E), the probability of not landing on yellow or a consonant will be,

P(E ∪ F)\' = 1 – P(E ∪ F)

               = 1 – 5/8

               = 3/8