Question

If you flip a coin and roll a $6$-sided die, what is the probability that you will flip a head and roll an even number?

Answer 1

Step 1. Find the probability to flip the head.

A coin has two sides head and a tail. While flipping a coin, the total outcome is $2$ and the favorable outcome for a head is $1$.

Now using the formula of probability find the probability of getting head.

$\begin{array}{rcl}P\left(\mathrm{Head}\right)& =& \frac{\mathrm{favorable}\mathrm{outcome}}{\mathrm{Total}\mathrm{outcomes}}\\ & =& \frac{1}{2}\end{array}$

Step 2. Find the probability to roll an even number.

A dice has 6 sides and there are $3$ even sides. The even sides are $2,4,\mathrm{and}6$. The total outcomes are $6$ and the favorable outcome for an even number is $3$. Now using the formula of probability find the probability of getting an even number.

$\begin{array}{rcl}P\left(\mathrm{Even}\mathrm{Number}\right)& =& \frac{\mathrm{favorable}\mathrm{outcome}}{\mathrm{Total}\mathrm{outcomes}}\\ & =& \frac{3}{6}\\ & =& \frac{1}{2}\end{array}$

Step 3. Find the probability to flip a head and roll an even number.

Since both given events are independent events, multiply both the probability to find the probability of getting head and roll an even number.

$\begin{array}{rcl}P\left(\mathrm{a}\mathrm{head}\mathrm{and}\mathrm{an}\mathrm{even}\mathrm{number}\right)& =& \frac{1}{2}·\frac{1}{2}\\ & =& \frac{1}{4}\end{array}$

Therefore, the obtained probability for the given event is $\frac{1}{4}$.