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5-18.

For each of the experimental results described, write the indicated probability.

Do you remember the difference between experimental and theoretical probability?
Here, you are trying to calculate the theoretical probability, or

$\large\frac{\text{Number of successful outcomes in the experiment}}{\text{Total number of outcomes in the experiment}}$

1. A coin is flipped $80$ times. It lands tails $47$ times. What is the $\text{P(heads)}$?

If the coin landed on tails $47$ times out of a total of $80$ times, how many times did the coin land on heads?

2. A bag contains purple and orange marbles. Sam randomly takes out one marble and then returns it to the bag. He does this $18$ times, and $12$ of those times an orange marble is pulled out. What is $\text{P(green)}$?

Read the situation carefully. How many green marbles are in the bag?

The probability is $0$ because there are no green marbles in the bag.

3. Sarah pulls a card from a standard deck and then replaces it. She does this $30$ times, and $40\%$ of the time it is hearts. What is the probability that she does not get hearts? (Note: For more information on standard card decks, refer to problem 4-19.)

The probability of not pulling a heart out of the deck can also be considered as the probability of pulling a card that is not a heart.

If she pulled hearts $40\%$ of the time out of $30$ attempts, how many hearts did she draw?

$\frac{40}{100}\cdot30=?$

Based on this number and the total number of cards, find the number of non-hearts that she drew and find its probability.

$60\%$ or $\frac{18}{30}$