A game involves tossing three coins. complete a tree diagram to show all the possible outcomes and find the probability of tossing exactly two heads.
There are 8 possible outcomes.
The outcomes with exactly two heads are HH T, HT H, TH H. So, the probability of tossing exactly two heads is 3/8 or 0.375.
To complete a tree diagram for tossing three coins, we start by drawing three branches from the initial node representing each coin toss. Each branch has two possible outcomes: either a "H" for heads or a "T" for tails. Let's draw the tree diagram:
_______
| |
H | T | H
__| _|___
| | | |
H | T | H | T | H
_|___|____|___|____|___
| | | | |
H | T | H | T | H | T
_|___|____|___|____|___|____
In this tree diagram, each path represents a different possible outcome. For example, the path "HTH" means heads on the first toss, tails on the second toss, and heads on the third toss.
To find the probability of tossing exactly two heads, we need to count the number of paths that have exactly two "H's" and divide it by the total number of possible outcomes.
From the tree diagram, we can see that there are three paths with exactly two heads: HHT, HTH, and THH.
Therefore, the probability of tossing exactly two heads is 3/8 or 0.375.