Chapter 5.3, Problem 105E

To determine

Probability for the die shows a 1.

Answer to Problem 105E

Probability that the die shows a 1 is 0.60.

Explanation of Solution

Given information:

Probability model for loaded die:

  

Calculations:

According to the addition rule for disjoint or mutually exclusive events,

  $P\left(\text{A}\cup \text{B}\right)=P\left(\text{A}\text{or}\text{B}\right)=P\left(\text{A}\right)+P\left(\text{B}\right)$

Conditional probability definition:

  $P\left(\text{B}|\text{A}\right)=\frac{P\left(\text{A}\cap \text{B}\right)}{P\left(\text{A}\right)}=\frac{P\left(\text{A}\text{and}\text{B}\right)}{P\left(\text{A}\right)}$

From the table,

Probability to roll a 1,

  $P\left(1\right)=0.3$

For the probability to roll an odd (1, 3 or 5),

Apply the addition rule for disjoint events:

  $P\left(\text{odd}\right)=P\left(1\right)+P\left(3\right)+P\left(5\right)=0.3+0.1+0.1=0.5$

Using conditional probability definition:

  $P\left(\text{1}|\text{odd}\right)=\frac{P\left(1\text{and}\text{odd}\right)}{P\left(\text{odd}\right)}=\frac{0.3}{0.5}=\frac{3}{5}=0.60$

Thus,

The conditional probability to roll 1 is 0.60.