Question

Christine has always been weak in mathematics. Based on her performance prior to the final exam in Calculus, there is a 63% chance that she will fail the course if she does not have a tutor. With a tutor, her probability of failing decreases to 33%. There is only a 73% chance that she will find a tutor at such short notice. a. What is the probability that Christine fails the course? (Round your answer to 4 decimal places.) b. Christine ends up failing the course. What is the probability that she had found a tutor? (Round your answer to 4 decimal places.)

Answer 1

Answer:

(a) The probability that Christine fails the course is 0.411.

(b) The probability that Christine finds a tutor given that she fails the course is 0.586.

Step-by-step explanation:

Let the events be:

X = Christine fails the course.

Y = Christine finds a tutor.

Given:

$P(X|Y)=0.33\\P(X|Y^{c})=0.63\\P(Y)=0.73$

(a)

Compute the probability that Christine fails the course as follows:

$P(X)=P(X|Y)P(Y)+P(X|Y^{c})P(Y^{c})\\=(0.33\times0.73)+(0.63\times[1-0.73])\\=0.411$

Thus, the probability that Christine fails the course is 0.411.

(b)

Compute the probability that Christine finds a tutor given that she fails the course as follows:

$P(Y|X)=\frac{P(X|Y)P(Y)}{P(X)}=\frac{0.33\times 0.73}{0.411}= 0.586$

Thus, the probability that Christine finds a tutor given that she fails the course is 0.586.