Question

assume that Pr[A ∪B] = 0.3 and Pr[A] = 0.2.
(1) What is Pr[B] if A and B are independent events?

Answer 1

Pr[A U B] = Pr[A] + Pr[B] - Pr[AB]

That's the definition you need. You also need to know the definition of independent events. You should be able to solve it in one or two lines after that.

Answer 2

im confused the disjoint is .1 so what is the independent?

Answer 3

Independence implies Pr[AB] = Pr[A]*Pr[B]

You may want to read your textbook. These definitions should be in there and are pretty important to solving these equations.

Answer 4

how do u know what b is when they only give u a

Answer 5

Also, disjoint implies Pr[AB] = 0. The intersection of two disjoint sets is empty.

You're solving for Pr[B].

Answer 6

i know u need to multiply the 2

Answer 7

so what is b?

Answer 8

I'm not giving you the answer. You have the equations you need. Plug in the numbers and solve it. I'll check your answer for you, if you'd like.

Answer 9

i got .1

Answer 10

that is the disjoint i need the independent

Answer 11

Again, use the definition: A and B independent implies Pr[AB] = Pr[A]*Pr[B]

Answer 12

would it be 0?

Answer 13

Not quite. Here, I'll write the equation for you:

P[A U B] = P[A] + P[B] - P[A]*P[B]

You're solving for P[B]. You know P[A] and P[A U B]. Just plug in the numbers.

Answer 14

i know its not working u can't do .1=x-.2x

Answer 15

i figured it out thanks

Answer 16

Good. :)