Chapter 5: Q. 41 (page 327)

Who eats breakfast?Students in an urban school were curious about how many children regularly eat breakfast. They conducted a survey, asking, “Do you eat breakfast on a regular basis?” All $595$ students in the school responded to the survey. The resulting data are shown in the two-way table.
Suppose we select a student from the school at random. Define event $F$ as getting a female student and event $B$ as getting a student who eats breakfast regularly.
a. Find $P (B^{C})$
b. Find $P (F a n d B^{C})$ . Interpret this value in context.
c. Find $P (F o r B^{C})$ .

Short Answer

Expert verified

a. Student who does not eat breakfast on a regular basis $0.4958$

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

c. The probability that a student is female or do not eats breakfast regularly is $0.6807$

Step by step solution

Part (a) Step 1 : Given Information

We have to compute the probability of $B^{C}$

Part (a) Step 2 : Simplification

Below is a two-way table showing gender and breakfast habits.

F

is the occurrence of a female student being chosen.

B

is the occurrence of a student who frequently eats breakfast.

The following formula was used:

$P (B^{C}) = \frac{N u m b e r o f s t u d e n t s w h o d o n o t e a t b r e a k f a s t r e g u l a r l y}{T o t a l n u m b e r o f s t u d e n t s}$

$B^{C}$ refers to a student who does not eat breakfast on a regular basis.

Between the two tables,

295

kids do not eat breakfast on a regular basis.

There are

595

pupils in all.

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

Part (b) Step 1 : Given Information

We have to compute the probability of $F$ and $B^{c}$

Part (b) Step 2 : Simplification

Female students do not eat breakfast on a daily basis is

165

The total number of pupils in the class is

595

$P (F a n d B^{c}) = \frac{165}{595} = 0.2773$

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

Part (c) Step 1 : Given Information

We have to compute $P (F a n d B^{c})$ .

Part (c) Step 2 : Simplification

The formula we use :

$P (F o r B^{c}) = P (F) + P (B^{c}) - P (F a n d B^{c}) P (F) = \frac{N u m b e r o f f e m a l e s t u d e n t s}{T o t a l n u m b e r o f s t u d e n t s}$