Exercise 40 Page 963

The two events described in this exercise are rolling a

2

on the first die and rolling a

3

on the second die. Since neither of these events affects the probability of the other, these are independent events. If two events are independent, then the probability of both occurring is the product of their individual probabilities.

P (A and B) = P (A) \cdot P (B)

Let's start by calculating the probability of rolling a

2

on a die.

A die has

6

sides and

1

of them is numbered two.

P (A) = \frac{1}{6} \leftarrow Sides numbered two \leftarrow Total sides

P (B)

is the probability of rolling a

3

on another die.

The second die also has

6

sides and

1

of them is numbered three.

P (B) = \frac{1}{6} \leftarrow Sides numbered three \leftarrow Total sides

Finally, according to the formula, to calculate

P (A and B)

we have to multiply

P (A)

and

P (B) .

P (A and B) = P (A) \cdot P (B)

SubstituteII

$P (A) = \frac{1}{6}$ , $P (B) = \frac{1}{6}$

P (A and B) = \frac{1}{6} \cdot \frac{1}{6}

MultFrac

Multiply fractions

P (A and B) = \frac{1}{3 6}

▼

Convert to percent

UseCalc

Use a calculator

P (A and B) = 0.02 \overline{7}

RoundDec

Round to $3$ decimal place(s)

P (A and B) \approx 0.028

WritePercent

Convert to percent

P (A and B) \approx 2.8 %

Probability of the given event is equal to

\frac{1}{3 6}

or about

2.8 % .