Christine has always been weak in mathematics. Based on her performance prior to the final exam in Calculus, there is a 65% chance that she will fail the course if she does not have a tutor. With a tutor, her probability of failing decreases to 35%. There is only a 75% chance that she will find a tutor at such short notice.
What is the probability that Christine fails the course?

the probability that Christine fails the course is 0.425

Step-by-step explanation:

A = Christine fails the course

B = Christine finds a tutor at such short notice

P(B) = 0.75

P(A|B) = 0.35

P(A|B') = 0.65

by total probability theorem

P(A) = P(A∩B) + P(A∩B')

by definition of intersection probability

P(A) = P(A|B)P(B) + P(A|B') P(B') = 0.35*0.75 + 0.65*(1-0.75)=0.425

- "runner b is moving at a slower rate."

- "the graphs shown are graphs of distance(km) against time(min).

the slopes of this graphs are are given by:

slope = (change in y)/(change in x)

= (change in distance)/(change in time)

this is the formula for finding the speed. so, the slope of these graphs represent the speed of the runner.

taking each division in the graph to represent 1 on both axis:

runner a ⇒ speed = (2-0)/(1-0)

= 2/1

= 2 km/min

runner b ⇒ speed = (3-0)/(3-0)

= 3/3

= 1 km/min

this shows that   runner b is moving at a slower rate."