Chapter 5.2, Problem 41E

To determine

(a)

To compute: Probability of B^c

Answer to Problem 41E

Probability of B^c is 0.4958.

Explanation of Solution

Given information:

The two way table of gender and breakfast habits is given below

		Gender
		Male	Female	Total
Eats breakfast regularly	Yes	190	110	300
	No	130	165	295
	Total	320	270	595

F is the event of a female student selected

B is the event of a student who eats breakfast regularly

Formula used:

  $\text{P}\left({{\displaystyle \text{B}}}^c\right)=\frac{\text{Number of students who do not eat breakfast regularly}}{\text{Total number of students }}$

Calculation:

B^c is the event of a student who does not eat breakfast regularly.

From the two table,

Number of students who do not eat breakfast regularly = 295

Total number of students = 595

  $P\left({{\displaystyle B}}^c\right)=\frac{295}{595}=0.4958$

(b)

To determine

To compute: The probability of F and B^c

Answer to Problem 41E

The required probability is 0.2773.

Explanation of Solution

Formula used:

  $P\left(F\text{ and }{{\displaystyle B}}^c\right)=\frac{\text{Number of female students who do not eat breakfast regularly}}{\text{Total number of students }}$

Calculation:

Number of female students who do not eat breakfast regularly = 165

Total number of students = 595

  $P\left(F\text{ and }{{\displaystyle B}}^c\right)=\frac{165}{595}=0.2773$

Interpretation:

The probability that a student is female and do not eats breakfast regularly is 0.2773.

To determine

(c)

To compute: P (F and B^c)

Answer to Problem 41E

The required probability is 0.6807.

Explanation of Solution

Formula used:

  $P\left(F\text{ or }{{\displaystyle B}}^c\right)=P(F)+P\left({{\displaystyle B}}^c\right)-P\left(F\text{ and }{{\displaystyle B}}^c\right)$

  $P\left(F\right)=\frac{\text{Number of female students }}{\text{Total number of students }}$

Calculation:

Number of female students = 275

Total number of students = 595

  $P\left(F\right)=\frac{275}{595}=0.4622$

P (F and B^c) = 0.4622 + 0.4958 − 0.2773 = 0.6807