Q: Are the events 'providing financial assistance to buy a car' and 'providing financial assistance to pay rent' independent? Use the probabilities from the table to justify your answer.

No, because $$ P(C \cap R) \neq P(C) \times P(R) $$

Q: If the probability that a parent provided financial assistance to buy a car is $$ 0.175 $$, and the probability that they provided financial assistance to pay rent is $$ 0.41 $$, what would be the probability that they provided both, if the events were independent?

$$ 0.175 \times 0.41 = 0.07175 $$

Question 1

Given the joint probability table for parents providing financial assistance to their adult children for buying a car and paying rent, what is the probability that a randomly selected parent provided financial assistance for both buying a car and paying rent?

Accepted Answer

$$ \frac{28}{200} = 0.14 $$

Question 2

If a parent did NOT provide financial assistance to buy a car, what is the probability that they assisted with paying rent?

Accepted Answer

$$ \frac{54}{86} \approx 0.628 $$

Question 3

What is the marginal probability that a parent provided financial assistance to pay rent?

Accepted Answer

$$ \frac{82}{200} = 0.41 $$

Question 4

Using the joint probability table, what is the probability that a parent provided financial assistance for buying a car, given that they provided financial assistance for paying rent?

Accepted Answer

$$ \frac{28}{82} \approx 0.341 $$

Question 5

Are the events 'providing financial assistance to buy a car' and 'providing financial assistance to pay rent' independent? Use the probabilities from the table to justify your answer.

Accepted Answer

No, because $$ P(C \cap R) 
eq P(C) 	imes P(R) $$

Question 6

If a parent provided financial assistance to buy a car, what is the probability that they also provided financial assistance to pay rent?

Accepted Answer

$$ \frac{28}{114} \approx 0.246 $$

Question 7

What is the probability that a parent did NOT provide financial assistance for either buying a car or paying rent?

Accepted Answer

$$ \frac{54}{200} = 0.27 $$

Question 8

Suppose you randomly select a parent who provided financial assistance to pay rent. What is the probability that they did NOT provide financial assistance to buy a car?

Accepted Answer

$$ \frac{54}{82} \approx 0.659 $$

Question 9

Which of the following best describes the concept of joint probability in the context of the table provided?

Accepted Answer

The probability that both events (providing financial assistance for buying a car and paying rent) occur together.

Question 10

If you want to find the probability that a parent provided financial assistance for at least one of the two expenses (buying a car or paying rent), which formula should you use?

Accepted Answer

$$ P(C) + P(R) - P(C \cap R) $$

Question 11

Given the probabilities $$ P(C) = 0.175 $$ and $$ P(R) = 0.41 $$, and $$ P(C \cap R) = 0.14 $$, what is the probability that a parent provided financial assistance for at least one of the two expenses?

Accepted Answer

$$ 0.175 + 0.41 - 0.14 = 0.445 $$

Question 12

If the probability that a parent provided financial assistance to buy a car is $$ 0.175 $$, and the probability that they provided financial assistance to pay rent is $$ 0.41 $$, what would be the probability that they provided both, if the events were independent?

Accepted Answer

$$ 0.175 	imes 0.41 = 0.07175 $$

Question 13

Based on the data, are parents more likely to provide financial assistance for buying a car if they have already provided financial assistance for paying rent?

Accepted Answer

Yes, because $$ P(C|R) \u003e P(C) $$

Question 14

If you want to test whether providing financial assistance for buying a car is independent of providing financial assistance for paying rent, which calculation would you perform?

Accepted Answer

Compare $$ P(C|R)  to$$ $$ P(C) $$

Question 15

What is the conditional probability that a parent provided financial assistance to pay rent, given that they did NOT provide financial assistance to buy a car?

Accepted Answer

$$ \frac{54}{86} \approx 0.628 $$

Question 16

If a parent did NOT provide financial assistance for paying rent, what is the probability that they provided financial assistance for buying a car?

Accepted Answer

$$ \frac{35}{118} \approx 0.297 $$

Question 17

Which of the following statements is TRUE based on the joint probability table?

Accepted Answer

The probability of providing financial assistance for both buying a car and paying rent is less than the probability of providing assistance for either expense alone.

Joint Probability Tables and Conditional Probability in Business Statistics

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