The two events described in this exercise are tossing a coin and rolling a 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 the coin landing on heads.

P (A) = \frac{1}{2} \leftarrow heads on a coin \leftarrow possible outcomes

Let's now find the probability of rolling a number greater than four. On a regular die, there are two numbers greater than

4,

5,

and

6 .

P (B) = \frac{2}{6} \leftarrow numbers greater than four \leftarrow possible outcomes

Finally, we multiply

P (A)

and

P (B) .

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

SubstituteII

$P (A) = \frac{1}{2}$ , $P (B) = \frac{2}{6}$

P (A and B) = \frac{1}{2} \cdot \frac{2}{6}

ReduceFrac

$\frac{a}{b} = \frac{a / 2}{b / 2}$

P (A and B) = \frac{1}{2} \cdot \frac{1}{3}

MultFrac

Multiply fractions

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

Extra

Simulations

A simulation can often help us understand the concepts that we learn related to probability. Here we can see the possible outcomes, as well as the random nature of these outcomes, when rolling a die.

Let's also see the possible outcomes and the random nature of these outcomes when flipping a coin.

In cases such as these, where the objects in question are easy to find, it is more fun to play just around with them! Learning math can be fun, and statistics and probability are the most real-life applicable topics you will see in your high school math courses. Go out and have fun experimenting with different probabilities!

Exercise