Chapter 12.6, Problem 13PPS

a.

To determine

To calculate the probability of rolling 2 on a dice, of rolling a 1 or a 6 on a dice, of rolling an odd number on a dice.

Answer to Problem 13PPS

The probability of rolling 2 on a dice is $\frac{1}{6}$

The probability of rolling 1 or 6 is $\frac{1}{3}$

The probability of rolling odd number is $\frac{1}{2}$

Explanation of Solution

Given information:

In a die, rolling a 2, rolling a 1 or 6, and rolling an odd number.

A dice consists of 6 number from 1 to 6 so consist 3 odd and 3 even number

Therefore, so the probability of rolling 2 on a dice is $\frac{1}{6}$

The probability a 1 or a 6 is equal to addition of probability of rolling 1 and probability of rolling 6.

Therefore, probability of rolling 1 or 6 is

  $\frac{1}{6}+\frac{1}{6}=\frac{2}{6}=\frac{1}{3}$

Therefore, probability of rolling odd number is

  $\frac{3}{6}=\frac{1}{2}$

b.

To determine

To roll the dice 20 times and record the value of the dice after each roll.

Answer to Problem 13PPS

After rolling a dice 20 times the result is,

  $1:6,2:3,4:0,3:7,5:2,6:2$

Explanation of Solution

Given information:

The die roll 20 times.

After rolling a dice for 20 times assume to get the following result,

1 is get six times, 2 is get three times, 3 is get seven times, 4 is get zero times, 5 is get two times, 6 is get two times.

Therefore, it can be written as

c.

To determine

To calculate the probability distribution for $X$ , when its value is equal to the value of the dice

Answer to Problem 13PPS

The table for the data is

1	0.3
2	0.15
3	0.35
4	0
5	0.1
6	0.1

Explanation of Solution

Given information:

The value of $X$ is equal to the value of the die.

Based on the result of rolling a dice 20 times,

Probability of getting 1 in 20 times is $\frac{6}{20}=0.3$

Probability of getting 2 in 20 times is $\frac{3}{20}=0.15$

Probability of getting 3 in 20 times is $\frac{7}{20}=0.35$

Probability of getting 4 in 20 times is $\frac{0}{20}=0$

Probability of getting 5 in 20 times is $\frac{2}{20}=0.1$

Probability of getting 6 in 20 times is $\frac{2}{20}=0.1$

Therefore, the table will be,

1	0.3
2	0.15
3	0.35
4	0
5	0.1
6	0.1

d.

To determine

To find why the number may not be same when the probability distribution is made on rolling a dice 2 times, on rolling 1 or 6 times and rolling to get an odd number

Answer to Problem 13PPS

The probability of rolling 2 is 15%

The probability of rolling 1 or 6 is 40%

The probability of rolling an odd number is 75%

The first set of probabilities have prediction based on everything being equal. The second set were based on actually that happened.

Explanation of Solution

Given information:

In a die, rolling a 2, rolling a 1 or 6, and rolling an odd number.

1	0.3
2	0.15
3	0.35
4	0
5	0.1
6	0.1

From this table,

Probability of rolling 2 is $0.15\text{ or }15\%$

Probability of rolling 1 or 6 is $\left(0.3+0.1\right)=0.4\text{ or }40\%$

Probability of rolling an odd number is $\left(0.3+0.35+0.1\right)=0.75\text{ or }75\%$

Therefore,

The first set of probabilities have prediction based on everything being equal. The second set were based on actually that happened.