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2-128.

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

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 1-68.)

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 $\frac{18}{30}$