Question

For the following exercises, use the spinner in Figure 1.

What is the probability of landing on anything other than blue or an odd number? 

Answer 1

Consider the spinner given in the text book. The spinner consists of seven colored sections and each section is labeled by a number.

The sample space for the given experiment is,

S = {B1, P2, G3, B4, R5, O6, Y7}

Hence, n(S) = 7

 

Assume that E represents the event of landing on an odd number. Then,

E = {B1, G3, R5, Y7}

Hence, n(E) = 4

 

Use the formula of probability of an event E,

P(E) = n(E)/n(S) ...... (1)

 

Using formula (1) P(E) = n(E)/n(S), the probability of landing on an odd number will be,

P(E) = 4/7

 

Assume that F represents the event of landing on blue. Then,

F = {B1, B4}

Hence, n(F) = 2

 

Using formula (1) P(E) = n(E)/n(S), the probability of landing on blue will be,

P(F) = 2/7

 

The event E ∩ F represents the event of landing on an odd number and blue. Then,

E ∩ F = {B1}

Hence, n(E ∩ F) = 1

 

Using formula (1) P(E) = n(E)/n(S), the probability of landing on an odd number and blue will be,

n(E ∩ F) = 1/7

 

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

P(E ∪ F) = P(E) + P(F) – P(E ∩ F) ...... (2)

 

Using formula (2), the probability of landing on an odd number or blue will be,

P(E ∪ F) = 4/7 + 2/7 – 1/7

              = 5/7

 

Use the complement law for the probability,

P(E\') = 1 – P(E) ...... (3)

 

Using formula (3), the probability of landing on anything other than odd number or blue will be,

P(E ∪ F)\' = 1 – P(E ∪ F)

               = 1 – 5/7

               = 2/7