1. ## Conditional probability

10. The following data from a sample of 100 families show the record of college attendance by fathers and their oldest sons: in 22 families, both father and son attended college; in 31 families, neither father nor son attended college; in 12 families, the father attended college while the son did not; and, in 35 families, the son attended college while the father did not.

a. What is the probability a son attended college given that his father attended college? 0.22 (3 pts)

b. What is the probability a son attended college given that his father did not attend college? 0.35 (3 pts)

My answers are wrong and I followed the joint probability formula..

2. Originally Posted by desire150
10. The following data from a sample of 100 families show the record of college attendance by fathers and their oldest sons: in 22 families, both father and son attended college; in 31 families, neither father nor son attended college; in 12 families, the father attended college while the son did not; and, in 35 families, the son attended college while the father did not.

a. What is the probability a son attended college given that his father attended college? 0.22 (3 pts)

b. What is the probability a son attended college given that his father did not attend college? 0.35 (3 pts)

My answers are wrong and I followed the joint probability formula..
a. Write F if the father attended college and S if the son attended college.

By the definition of conditional probability,
$\displaystyle P(S | F) = \frac{P(F \text{ and } S)}{P(F)} = \frac{0.22}{0.22 + 0.12}$
which is approximately 0.647.

3. ## Conditional Probability

Thank you very much for helping me out. I will use the formula provided to finish the question.

thank you again.

4. Using the formula provided, here is the answer I came up with. Please let me kow if this is correct or incorrect?
What is the probability a son attended college given that his father did not attend college

0.614

5. Hello, desire150!

The following data from a sample of 100 families show the record of college attendance by fathers and their oldest sons:
in 22 families, both father and son attended college.
in 31 families, neither father nor son attended college.
in 12 families, the father attended college while the son did not.
in 35 families, the son attended college while the father did not.

(a) What is the probability a son attended college, given that his father attended college?

(b) What is the probability a son attended college, given that his father did not attend college?

Tabulate the facts and their probabilities.

. . $\displaystyle \begin{array}{c||c||ccc} & \text{College} & & \\ \hline\hline \text{Father \& son} & 22 & P(F \wedge S) &=& 0.22 \\ \text{Father only} & 12 & P(F \wedge \sim\!S) &=& 0.12 \\ \text{Son only} & 35 & P(\sim\!F \wedge S) &=& 0.35 \\ \text{Neither} & 31 & P(\sim\!F \wedge \sim\!S) &=& 0.31 \\ \hline \end{array}$

Now you can use Bayes' Theorem to answer the questions.

. . $\displaystyle \begin{array}{cccc}(a) &P(S\,|\,F) &=& \dfrac{P(S \wedge F)}{P(F)} \\ \\[-3mm] (b) & P(S\,|\,\sim\!F) &=& \dfrac{P(S \wedge \sim\!F)}{P(\sim\!F)} \end{array}$

6. Thank you so much for the response. Here are my answerws using the formulas

a) .22
_________
.22+.12 =0.647

b)
.35
_____
.35+.31 = 0.530

Thank you. I'm finally getting his now..

7. ## Re: Conditional probability

Is attending college by the son independent of whether his father attended college?

8. ## Re: Conditional probability

Originally Posted by supriti
Is attending college by the son independent of whether his father attended college?
Does $\mathcal{P}(F\cap S)=\mathcal{P}(F)\cdot\mathcal{P}(S)~?$

9. ## Re: Conditional probability

P(F) = 0.22 + 0.12 = 0.34
P(S) = 0.22+0.35 = 0.57
P(F).P(S) = 0.1938
P(F∩S) = 0.22
So they are not same

10. ## Re: Conditional probability

Well what does that tell you?

11. ## Re: Conditional probability

Got it. Thanks.