Question

A and B are two candidates seeking admission in the college. The probability that A is selected is the 0.5 and the probability that both and B are selected is utmost 0.3 Show that the probability of B being selected is utmost 0.8

Answer 1

since prob of getting admission by A or B = 1.
so, using equn.
p(A U B) = p(A) + p(B) + p(A n B)

p(B) <= 0.8

Answer 2

Answer:

The proof is explained step-wise below :

Step-by-step explanation:

P(A) = 0.5

P(A ∩ B) ≤ 0.3

Now, using the relationship between the probability of two events

⇒ P(A) + P(B) - P(A ∩ B) = P(A ∪ B)

⇒ 0.5 + P(B) - P(A ∩ B) = 1

⇒ P(B) - P(A ∩ B) = 0.5

⇒ P(B) = 0.5 + P(A ∩ B)

⇒ P(B) ≤ 0.5 + 0.3

⇒ P(B) ≤ 0.8

Thus, The Probability of B being selected is at most 0.8

Hence Proved.