Question

Make an organized list to show all possible outcomes when four fair coins areflipped. Each coin lands facing either heads up (H)or tails up (T). What is theprobability that at least three coins land facing tails up?

Answer 1

Let's make a list to show all possible outcomes when four fair coins are flipped.

When four coins are flipped, we have the following outcomes:

The list can also be written in the form below:

HHHH, HHHT, HHTH, HHTT, HTHH, HTHT, HTTH, HTTT, THHT, THHH THTT, TTHH, TTHT, THTH, TTTT, TTTH

From the list we can see that there are 16 possible outcomes when four fair coins are flipped.

Let's find the probability that at least 3 coins land facing tails up.

From the list, the outcomes which at least 3 coins land facing tails up are 5.

They are:

HTTT, TTTH, THTT, TTHT and TTTT

Thus, we have:

Total number of outcomes = 16

Number of oucomes with at least 3 coins facing tails up = 5

To find the probability, we have:

`\begin{gathered} \text{ P(at least 3 coins tails up) = }\frac{\text{outcomes with at least 3 tails up}}{\text{Total outcome}} \\ \\ \text{ P(at least 3 tails up) = }(5)/(16) \end{gathered}`

ANSWER:

`(5)/(16)`