Chapter 8, Problem 25CT

(a)

To determine

To find the probability of both the numbers being picked as odd between $1$ and $60$ .

Answer to Problem 25CT

Theprobability of both the numbers being odd is $\frac{1}{4}$ .

Explanation of Solution

Given: Odd integers between $1$ and $60$ .

Formula Used:

Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur or how likely it is that a proposition is true.

Calculation:

Given:Odd integers between $1$ and $60$ .

From the above definition of probability, we have:

Probability of both the numbers being odd $=$ Probability of first number being odd $\times$ Probability of second number being odd

Probability of both the numbers being odd $=$ $\frac{30}{60}\times \frac{30}{60}$

The probability of both the numbers being odd $=$ $\frac{1}{4}$

Conclusion:

Hence, the probability of both the numbers being odd is $\frac{1}{4}$ .

(b)

To determine

To find the probability of both the numbers being picked is less than $12$ in between $1$ and $60$

Answer to Problem 25CT

The probability of both the numbers being less than 12 is $\frac{121}{3600}$ .

Explanation of Solution

Given: Both the numbers being less than $12$ between $1$ and $60$ .

Formula Used:

Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur or how likely it is that a proposition is true.

Calculation:

Given:Both the numbers being less than $12$ between $1$ and $60$ .

From the above definition of probability, we have:

Probability of both the numbers being less than $12$ between $1$ and $60$

  $=$ Probability of first number being less than $12$

  $\times$ Probability of second number being less than $12$

Probability of both the numbers being less than $12$

  $=$ $\frac{11}{60}\times \frac{11}{60}$

The probability of both the numbers being less than $12$

  $=$ $\frac{121}{3600}$

Conclusion:

Hence, the probability of both the numbers being less than 12 is $\frac{121}{3600}$ .

(c)

To determine

To find the probability of both the numbers being chosen same in between $1$ and $60$ .

Answer to Problem 25CT

The probability of both the numbers being chosen same is $\frac{1}{60}$ .

Explanation of Solution

Given: Both the numbers being chosen same between $1$ and $60$ .

Formula Used:

Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur or how likely it is that a proposition is true.

Calculation:

Given:Both the numbers being chosen same between $1$ and $60$ .

From the above definition of probability, we have:

Probability of both the numbers being chosen same between $1$ and $60$

  $=$ Probability of first number being chosen same $\times$ Probability of second number being chosen same

Probability of both the numbers being chosen same $=$ $\frac{60}{60}\times \frac{1}{60}$

The probability of both the numbers being chosen same $=$ $\frac{1}{60}$

Conclusion:

Hence, the probability of both the numbers being chosen same is $\frac{1}{60}$ .