Questions: Draw a tree diagram on a separate sheet of paper. Then find the probability. 6. P(H, 5) 7. P(T, 2) 8. P(T, even) 9. P(H, odd) 10. P(T, 2 or 3) 11. P(H, not 2) Heads (H)

Draw a tree diagram on a separate sheet of paper. Then find the probability. 6. P(H, 5) 7. P(T, 2) 8. P(T, even) 9. P(H, odd) 10. P(T, 2 or 3) 11. P(H, not 2) Heads (H)
Transcript text: Draw a tree diagram on a separate sheet of paper. Then find the probability. 6. $P(H, 5)$ $\qquad$ 7. $P(T, 2)$ $\qquad$ 8. $P(T$, even $)$ $\qquad$ 9. $P(H, o d d)$ $\qquad$ 10. $P(T, 2$ or 3$)$ $\qquad$ 11. $P(H$, not 2$)$ $\qquad$ Heads (H)
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Solution

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Solution Steps

Step 1: Analyze the Problem

We are given a spinner with 5 equally likely outcomes: 1, 2, 3, 4, and 5. We also have a coin flip with two equally likely outcomes: Heads (H) and Tails (T). We need to calculate probabilities involving both the coin flip and the spinner.

Step 2: Construct the Tree Diagram (Conceptual)

While we are asked to draw a tree diagram on paper, we can conceptualize it here. The first branch of the tree represents the coin flip (H or T). Each of these branches then has 5 sub-branches representing the spinner outcomes (1, 2, 3, 4, 5). This creates a total of 10 possible outcomes: (H,1), (H,2), (H,3), (H,4), (H,5), (T,1), (T,2), (T,3), (T,4), and (T,5).

Step 3: Calculate P(H, 5)

The probability of getting heads and landing on 5 is the number of favorable outcomes (H,5) divided by the total number of outcomes. Since there's one (H,5) outcome and ten total outcomes, the probability is 1/10.

Step 4: Calculate P(T, 2)

The probability of getting tails and landing on 2 is the number of favorable outcomes (T,2) divided by the total number of outcomes. There's one (T,2) outcome and ten total outcomes, so the probability is 1/10.

Step 5: Calculate P(T, even)

The favorable outcomes are (T,2) and (T,4). There are two favorable outcomes and ten total outcomes, so the probability is 2/10, which simplifies to 1/5.

Final Answer

P(H, 5) = 1/10 P(T, 2) = 1/10 P(T, even) = 1/5

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