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}}=(1)/(2)\cdot(1)/(2)=(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}}=(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}=(2)/(6)\cdot(1)/(6)=(2)/(36)=(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}=(1)/(4)\cdot(1)/(18)=(1)/(72)\approx0.0139`

The probability is 1.39%