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.)

(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:

(a)

Compute the probability that Christine fails the course as follows:

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:

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

solution:

→c= a b , that is product of a and b is possible only when when a is m × n matrix and b is n × p matrix.

that is, number of columns of a= number of rows of b.

so, size of matrix , c= a b is , if a = (m × n)matrix

b= (n × p)matrix

then a b = [ (m × n)matrix] ×[   (n × p)matrix ]

→→c= a b= [m × p ] matrix

→→size of product a b will be equal to = number of rows of a × number of columns of b