Question

Let A and B be two events such that P (A) = 0.68 and P(B) = 0.01. Do not round your responses. (If necessary, consult a list of formulas.) (a) Determine P (AUB), given that A and B are independent. U (b) Determine P (AUB), given that A and B are mutually exclusive. X 5 ?

Answer 1

Given that P(A)=0.68 and P(B)=0.01.

(a) We have to determine the value of P(A U B) when A and B are independent.

We know that when two events A and B are independent,

$P(A \cap B ) = P(A)P(B)$

Now , we also know that

...................................(1)

P(AUB) = P(A) + P(B) - PANB

  

  

  

  

(b) Now in the second case, we are required to find the value of P(A U B) when A and B are mutually exclusive.

When two events A and B are mutually exclusive,

P(ANB) = 0

So,

$P(A \cup B)=P(A)+P(B)-0$ [by using the formula in (1)]

  $=P(A)+P(B)$

  $=0.68+0.01$

  $=0.69$

Please leave a comment if there is any doubt. There are two different answers for the two different cases.

All the steps and explainations are given.

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