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Math OER
Week 9 Activity

Practice with Contingency Tables and Conditional Probability

Show your work or explain your thinking. There may be a few different methods that work.

1. According to the 2019 U.S. Census, the country's total population was 328,239,523 people. The Census only uses male and female genders: 50.8% of the population was female, and the rest male. The census does not ask about handedness, but other studies estimate 11.8% of males are left-handed, and 9.6% of females are left-handed. Use this information to fill out the table below.

FemaleMaleTotal
Right Handed
Left Handed
Total

For the follwing problems, use the following labels for situations: L = left handed, R = right handed, M = male, and F = female.

2. The statement "11.8% of males are left-handed" can be rephrased as the probability a person is left-handed, given that the person is male, is 11.8%. The notation for this conditional probability is P(L|M) and we could write the equation P(L|M) = 0.118. Write a similar equation for the statement "9.6% of females are left-handed".

3. Would you say that gender and handedness are independent? That is, does one’s gender affect one’s likelihood of being left handed or right handed?

4. Recall that for independent events A and B, P(A and B) = P(A) × P(B). Can we say that P(M and L) = P(M) × P(L)?

5. n general, if events A and B are not independent, then we write P(A and B) = P(A) × P(B|A). Knowing L and M are not independent, write P(M and L) as a product.

6. Knowing L and F are not independent, write P(F and L) as a product.

7. The DSM-5 estimates that 0.005% to 0.014% of male newborns will experience gender dysphoria at some time in their life. Studies have linked high levels of maternal first-trimester intrauterine testosterone to both left-handedness and gender dysphoria. Furthermore, a 2001 study found 19.5% of its boys with gender dysphoria were left-handed. Use this information to fill out the table below for Oregon's population of 700,000 boys of age 14 years or younger.

Boys without Gender DysphoriaBoys without Gender DysphoriaTotal
Right Handed
Left Handed
Total

For the follwing problems, use the following labels for situations: L = left handed, R = right handed, N = boy without Gender Dysphoria, and Y = boy with Gender Dysphoria.

8. Find low and high estimates of P(L|N).

9. Find low and high estimates of P(N|L).

10. Find low and high estimates of P(L|Y).

11. Find low and high estimates of P(Y|L).

12. Remind yourself about the probability "or" formula, and then find low and high estimates of P(Y or L).

Practice with Likelihood and Expected Value

1. A charity is holding a raffle, selling 300 tickets. The ticket costs $5. The one winning ticket holder gets $500. What is the expected value for a person buying one ticket?

OutcomeNumeric ValueProbabilityProduct
Win
Lose
Expected Value:

2. If there were three winning tickets for $500 each, what would be the expected value for a person buying one ticket?

OutcomeNumeric ValueProbabilityProduct
Win
Lose
Expected Value:

For the following questions, write your answer as (a) a fraction, (b) a decimal with 2 decimal places, and finally (c) a percentage rounded to the nearest whole percent.

3a. The table below shows the number of credit cards owned by a group of individuals. If one person was chosen at random, find the probability that the person was female.

ZeroOneTwo or MoreTotal
Male951933
Female18102048
Total27153981

3b. If one person was chosen at random, find the probability that the person was male and had two or more credit cards.

3c. If one person was chosen at random, find the probability that the person was male or had two or more credit cards.

3d. If one person with zero credit cards was chosen at random, find the probability that the person was female.

3e. If one person who is female was chosen at random, find the probability that the person was had zero credit cards.

These problems are not graded. They are only to help you practice with our math topics. Do not rush to look at answers! First ask for hints from your instructor or classmates. But if you are really ready, the answers are here. (Answers not ready yet.)