7. When Mendel conducted his famous genetics experiments with peas, one sample of offspring
consisted of 428 green peas and 152 yellow peas. Based on those results, estimate the probability of
getting an offspring pea that is green. Is the result reasonably close to the expected value of 3
4 as
claimed by Mendel?
8. In a New York Times/CBS News poll, respondents were asked if it should be legal or illegal to use a
hand-held cell phone while driving. 141 said that it should be legal, and 663 said that it should be
illegal. What is the probability of randomly selecting someone who believes it should be legal to use a
hand-held cell phone while driving? Is it unlikely to randomly select someone with that belief?
9. Here is the sample space listing the eight simple events that are possible when a couple has three
children:
GGG GGB GBG BGG
BBB BBG BGB GBB
Assume that boys and girls are equally likely, so that the eight simple events are equally likely. Find the
probability that when a couple has three children, there is exactly one girl.
10. Using the same sample space from question 9, find the probability that when a couple has three
children, there are exactly two girls.


### Problem 7:
To estimate the probability of getting a green pea, use the following formula for empirical probability:

\[
P(\text{green pea}) = \frac{\text{number of green peas}}{\text{total number of peas}} = \frac{428}{428 + 152} = \frac{428}{580}
\]

Simplifying:

\[
P(\text{green pea}) = 0.7379
\]

Now compare this result to Mendel's expected probability of \(\frac{3}{4} = 0.75\). The empirical probability (0.7379) is very close to 0.75, meaning the result is reasonably close to Mendel's expected value.

### Problem 8:
The probability of selecting someone who believes it should be legal to use a hand-held cell phone while driving is given by:

\[
P(\text{legal}) = \frac{\text{number who believe it should be legal}}{\text{total number of respondents}} = \frac{141}{141 + 663} = \frac{141}{804}
\]

Simplifying:

\[
P(\text{legal}) \approx 0.1754
\]

Since the probability of randomly selecting someone who believes it should be legal is approximately 0.1754 (or 17.54%), it is not extremely low, but it is less likely compared to the majority who believe it should be illegal.

### Problem 9:
The sample space for three children (GGG, GGB, GBG, BGG, BBB, BBG, BGB, GBB) consists of 8 equally likely events. We want to find the probability of having exactly one girl.

The events with exactly one girl are: **GBB, BGB, BBG**.

There are 3 favorable outcomes, so the probability is:

\[
P(\text{exactly one girl}) = \frac{\text{number of favorable outcomes}}{\text{total number of outcomes}} = \frac{3}{8}
\]

Thus, the probability is \(\frac{3}{8} = 0.375\).

### Problem 10:
Now we want the probability of having exactly two girls.

The events with exactly two girls are: **GGB, GBG, BGG**.

There are 3 favorable outcomes, so the probability is:

\[
P(\text{exactly two girls}) = \frac{\text{number of favorable outcomes}}{\text{total number of outcomes}} = \frac{3}{8}
\]

Thus, the probability is also \(\frac{3}{8} = 0.375\).

---

Do you want any details or further clarification? Here are some related questions you can explore:

1. What factors could cause the empirical probability in Mendel's experiment to differ from the expected value?
2. How do we interpret probabilities that are "reasonably close" to expected values in experiments?
3. How can you calculate the margin of error for empirical probability estimates?
4. What are the ethical and practical implications of banning hand-held cell phones while driving?
5. How do we calculate probabilities when the events are not equally likely?

**Tip:** In probability problems, carefully count favorable outcomes and compare them to total possible outcomes for clarity.

7. When Mendel conducted his famous genetics experiments with peas, one sample of offspring consisted of 428 green peas and 152 yellow peas. Based on those results, estimate the probability of getting an offspring pea that is green. Is the result reasonably close to the expected value of 3/4 as claimed by Mendel? 8. In a New York Times/CBS News poll, respondents were asked if it should be legal or illegal to use a hand-held cell phone while driving. 141 said that it should be legal, and 663 said that it should be illegal. What is the probability of randomly selecting someone who believes it should be legal to use a hand-held cell phone while driving? Is it unlikely to randomly select someone with that belief? 9. Here is the sample space listing the eight simple events that are possible when a couple has three children: GGG GGB GBG BGG BBB BBG BGB GBB Assume that boys and girls are equally likely, so that the eight simple events are equally likely. Find the probability that when a couple has three children, there is exactly one girl. 10. Using the same sample space from question 9, find the probability that when a couple has three children, there are exactly two girls.

Explore probability concepts through real-world examples like Mendel's pea experiments and survey polls on cell phone use while driving. Learn how to calculate empirical probabilities and interpret results based on data from experiments and polls.

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