The probability that a person visiting a zoo will see the giraffe is 0.72, the probability that he will see the bears is 0.84

Question

State whether the statement are True or False.

The probability that a person visiting a zoo will see the giraffe is 0.72, the probability that he will see the bears is 0.84 and the probability that he will see both is 0.52.

Answer 1

Let E₁ = Event person will see the giraffe

and E₂ = Event person will see the bear

Then, we have

P(E₁) = 0.72 and P(E₂) = 0.84

P(person will see both giraffe and bear) = 0.52

By General Addition Rule,

P(A ⋃ B) = P(A) + P (B) – P(A ⋂ B)

⇒ P(E₁⋃ E₂) = P(E₁) + P(E₂) – P(E₁⋂ E₂)

= 0.72 + 0.84 – 0.52

= 1.04 ≠ 0.52

Hence, the given statement is False.