Question

You flip two fair coins and roll two fair dice. What is the probability that you flip two tails and roll a 4 and a 5? Record the answer to the nearest hundredth of a percent

Answer 1

We flip two fair coins, the probability to get two tails is:

$p_{\text{tails}}=\frac{1}{2}\cdot\frac{1}{2}=\frac{1}{4}_{}$

The probability that a coin flip a tail is 1/2, so the probability that both coins flip tails is the product of the individuals probabilities, 1/2*1/2=1/4.

The probability that a dice roll any number is:

$p_{\text{dice}}=\frac{1}{6},\text{because the dice has 6 different numbers}$

The probability that two dice roll a 4 and a 5 is the product of 2/6*1/6. because we can get a 4 and a 5 or a 5 and a 4, so:

$p_{\text{dice-}4-5}=\frac{2}{6}\cdot\frac{1}{6}=\frac{2}{36}=\frac{1}{18}$

The probability of the both events together is the product of their probabilities, so:

$p=p_{\text{tails}}\cdot p_{\text{dice-}4-5}=\frac{1}{4}\cdot\frac{1}{18}=\frac{1}{72}\approx0.0139$

The probability is 1.39%