A coin is tossed three times. Use a tree diagram to find the number of possible outcomes that could produce exactly two heads.
I don't know how to write out a tree diagram on here, but I think this one is heads -> heads, tails -> heads, heads -> tails?
A quarter and a penny are tossed. Then an eight sided die is rolled. How many possible outcomes are there?
I'm getting 32 for this one, but I'm not sure if I'm doing it right? 2*2*8?
Oops, I meant to write heads, heads, tails. Heads, tails, heads. Tails, tails, heads. Although it looks to me that there could be more combinations?
tails, tails, heads does NOT work
H H T
H T H
T H H
Quarter, Penny could be
H H
H T
T H
T T
that is four, 8 now for each so 32 so I agree
For the first question, you are correct with the possible outcomes for getting exactly two heads: "HHH," "HHT," and "THH." So, there are 3 possible outcomes.
For the second question, you are almost correct. To find the total number of possible outcomes, you need to multiply the number of outcomes for each individual event.
The coin toss has 2 possible outcomes (heads or tails) and the coin is tossed twice. So, there are 2 * 2 = 4 possible outcomes for the coin toss.
The eight-sided die has 8 possible outcomes.
To find the total number of possible outcomes, you need to multiply the number of outcomes for each event:
Total number of outcomes = (Number of outcomes for coin toss) * (Number of outcomes for coin toss) * (Number of outcomes for die roll) = 4 * 8 = 32.
So, you were correct after all. There are indeed 32 possible outcomes.
For the first question about tossing a coin three times, you are correct in thinking that one possible outcome could be: heads -> heads, tails -> heads, heads -> tails. To find the number of possible outcomes that could produce exactly two heads, you need to consider all the different combinations.
One way to visualize this is by drawing a tree diagram. Start with the first toss and branch out for each possible outcome. Here's how it would look:
Toss 1
/ \
Heads Tails
/ \ / \
Heads Tails Heads Tails
| | |
H1 H2 H3
In this diagram, H1, H2, and H3 represent the three different possible outcomes of getting heads on the first toss. The total number of branches would be 8, indicating all the possible combinations of the three coin tosses.
To find the outcomes that produce exactly two heads, you need to count the number of paths that have two "H" branches. In this case, you have three paths that satisfy this condition: H1 -> Tails -> Heads, Tails -> H2 -> Heads, and H3 -> Tails -> Heads. Therefore, the number of possible outcomes that could produce exactly two heads is 3.
For the second question about tossing a quarter, a penny, and rolling an eight-sided die, you are correct in thinking that there are 2 possible outcomes for each coin toss, and 8 possible outcomes for the die roll.
To find the total number of possible outcomes, you can multiply the number of possibilities for each event together: 2 (coin toss) * 2 (coin toss) * 8 (die roll) = 32. Therefore, there are 32 possible outcomes in this scenario.