Question

The probability of a student scoring 75% in class work is 0.64, and the probability of a student scoring 85% is 0.45.

Event A: The student scores 75%.
Event B: The student scores 85%.

The probability of a student scoring 85% in class work, given that they have already scored 75% in class work, is 0.55. The probability of a student scoring 75% in class work, given that they have already scored 85% in class work, is 1.
Which statement is true?

Answer 1

if a student scored 85% it is sure that he scored 75% too
so the second statement is absolutely true

Answer 2

Events A and B are independent because P(A|B) = P(A).
Events A and B are independent because P(A|B) = P(B).
Events A and B are independent because P(A|B) = P(A) + P(B).
Events A and B are not independent because P(A| B) ≠ P(A).
Events A and B are not independent because P(A|B) = P(A).

Answer 3

two events are independent if P(A|B) = P(A)

here P(A|B) = 1 ≠ P(A) then Events A and B are not independent

Answer 4

i still dont understand how to solve this.

Answer 5

the first part is logical.. logically if it is given that a student scored 85% then he absolutely score more than 75%
thus P(A|B) = 1

for the second part you have to find if they are independent or not
two events A & B are independent if P(A|B) = P(A)
P(A|B) = 1
P(A) = 0.64
thus P(A| B) ≠ P(A) and A & B are not independent
so Events A and B are not independent because P(A|B) ≠ P(A)

Answer 6

i see, thanks.

Answer 7

welcome :)

Answer 8

so what was the answer? @yomylola @hoblos

Answer 9

D