Question

the probability that a student passes physics testis 2/3 and the probability that he passes both a physics test and english test is 14 /45the probability that he passes at least one test is 4/5 what is the probability that he passes the english test​

Answer 1

ANSWER:

Let's denote P(A)P(A) - probability to pass Physics test;

P(B)P(B) - probability to pass English test;

P(A\cap B)P(A∩B) - probability to pass both Physics and English tests;

P(A \cup B)P(A∪B) - probability to pass at least one test.

P(A \cup B) = P(A) + P(B) - P(A \cap B) \Rightarrow P(B) = P(A \cup B) - P(A) + P(A \cap B)P(A∪B)=P(A)+P(B)−P(A∩B)⇒P(B)=P(A∪B)−P(A)+P(A∩B).

P(B) = \frac{4}{5} - \frac{2}{3} + \frac{14}{45} = \frac{36-30+14}{45} = \frac{20}{45}P(B)=54−32+4514=4536−30+14=4520.

Answer: \frac{20}{45}4520.