Chapter 12.8, Problem 43PPE

a.

To determine

To find the probability that both the students are left handed.

Answer to Problem 43PPE

  $\frac{1}{19}$

Explanation of Solution

Given:

There are left handed and right handed students in a class room.

Calculation:

Consider the statement given in the question:

Let us take a sample of $20$ .

Now, look for the below given table:

  

Total number students are $20$ .

Number of left handers $5$

So,

  $\begin{array}{l}P(\text{left hander)}=\frac{5}{20}\\ =\frac{1}{4}\end{array}$

After choosing a left hander the number of students left is $19$ .

Thus, P (left hander, left hander):

  $\frac{1}{4}\times \frac{4}{19}=\frac{1}{19}$

b.

To determine

To find the probability that both the students are right handed.

Answer to Problem 43PPE

  $\frac{21}{38}$

Explanation of Solution

Given:

There are left handed and right handed students in a class room.

Calculation:

Consider the statement given in the question:

Let us take a sample of $20$ .

Now, look for the below given table:

  

Total number students are $20$ .

Number of right handers $15$

So,

  $\begin{array}{l}P(\text{right hander)}=\frac{15}{20}\\ =\frac{3}{4}\end{array}$

After choosing a right hander the number of students left is $19$ .

Thus, P(right hander, right hander):

  $\frac{3}{4}\times \frac{14}{19}=\frac{21}{38}$

c.

To determine

To find the probability that first student is left handed and the second student is right handed.

Answer to Problem 43PPE

  $\frac{15}{76}$

Explanation of Solution

Given:

There are left handed and right handed students in a class room.

Calculation:

Consider the statement given in the question:

Let us take a sample of $20$ .

Now, look for the below given table:

  

Total number students are $20$ .

Number of right handers $15$

So,

  $\begin{array}{l}P(\text{right hander)}=\frac{15}{20}\\ =\frac{3}{4}\end{array}$

After choosing a right hander the number of students left is $19$ .

Thus, P(right hander, left hander):

  $\frac{3}{4}\times \frac{5}{19}=\frac{15}{76}$