Final answer:
In Jill's game with a spinner and a coin, there are 10 possible outcomes. The probability of landing on purple or getting tails is 7 out of 10, and the probability of not landing on yellow and getting heads is 4 out of 10.
Step-by-step explanation:
Jill is playing a game where she uses a spinner divided into 5 equal sections and a fair coin. The first part of the question asks: How many possible outcomes are there in this scenario? Since the spinner has 5 sections and the coin has 2 possible outcomes, we multiply the number of outcomes for each to get the total number of possible outcomes. This gives us 5 (for the spinner) × 2 (for the coin) = 10 possible outcomes.
The next part of the question asks: What is the probability the spinner lands on purple or the coin lands on tails? We find this probability by adding the chance of the spinner landing on purple (which is 1 out of 5) to the chance of the coin landing on tails (which is 1 out of 2), but since the probability of both events happening together has been included in both individual probabilities, we need to subtract the joint probability (1/5 × 1/2). Thus the calculation is (1/5 + 1/2) - (1/10), which equals 7/10 or 70%.
Lastly, what is the probability the spinner does not land on yellow and the coin lands on heads? The probability the spinner does not land on yellow is 4 out of 5 (since there are 4 other colors), and the probability the coin lands on heads is 1 out of 2. Since these are independent events, we just multiply the probabilities: (4/5) × (1/2) = 4/10 or 40%.