Question

1st toss 2nd toss 3rd toss outcomes this tree diagram shows all the possible outcomes for tossing a coin three times. how many possible outcomes are there when a coin is tossed 3 times? how many outcomes include exactly one tail? 1 2 3 7

Explanation:

Step1: Count total outcomes

By observing the tree - diagram, we can list all outcomes. Each toss has 2 possibilities (H or T). For 3 tosses, we can also use the multiplication principle: \(2\times2\times2 = 8\). The outcomes are (H,H,H), (H,H,T), (H,T,H), (H,T,T), (T,H,H), (T,H,T), (T,T,H), (T,T,T).

Step2: Count outcomes with exactly one tail

We check each outcome. The outcomes with exactly one tail are (H,H,T), (H,T,H), (T,H,H). So there are 3 such outcomes.

Answer:

How many possible outcomes are there when a coin is tossed 3 times? 8
How many outcomes include exactly one tail? 3