Events A and B are independent. P(A)=0.4 and P(B)=0.3. Find P(A∪B) to two decimal places.

Question

anonymous · Answer

since A and B are independent, $$P(A \cup B) = P(A) + P(B)$$

anonymous · Answer

i thought it was P(a) + P(b) - ((P(a)*P(b))

anonymous · Answer

sorry my bad, that's if they are mutually exclusize

anonymous · Answer

yes, since A and B are independent $$P(A \cap B) = P(A) * P(B)$$

kropot72 · Answer

$$P(A \cup B)=0.4+0.3-(0.4\times 0.3)$$

deoxna · Answer

@kropot72  but how do you know they are combined events?

kropot72 · Answer

If A and B are two events, then A union B is the event A or B (or both). The probability of A or B is given by:
$$P(A \cup B)=P(A)+P(B)-P(A\ intersection\  B)$$

deoxna · Answer

But how do you know they are not mutually exclusive? Events can be both independent and mutually exclusive... (sorry if I'm being a pain but I really do want to get this)

kropot72 · Answer

Events A and B are independent if, and only if,
$$P(A\ intersection\ B)=P(A)\times P(B)$$
If A and B are mutually exclusive events the probability of A and B occurring is zero,
$$P(A\ intersection\ B)=0$$
In this question it is given that events A and B are independent.

deoxna · Answer

Wow, I really need to brush up on my probability... Ok thanks!