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In: Advanced Math

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?

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?

Solutions

Expert Solution

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

Junaid answered 1 year ago

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