s1: probability stuck on question

Hi, I'm not struggling with a question from my textbook, the answer is P(B=0.5 which works but I don't know how to get it

The only way I could think about doing it would be trial and error which obviously isn't going to get me a good answer!

I was thinking you could do 0.6xP(B) + 0.4xP(B) + 0.6xP(B') =0.7 but that wouldn't work would it as how can we assume P(B)=P(B')?

I'm assuming this is Q12:

Use the formula : $P(\text{A or B or both}) = P(A) + P(B) - P(\text{A and B})$

Usually written with symbols : $P(A\cup B) = P(A) + P(B) - P(A \cap B)$


Also, since A and B are independent you have the formula

$P(\text{A and B}) = P(A) \times P(B)$

Sorry I meant q11, but it seeems like you answered q11?

Sorry what does the cup mean? and/or ?

Yes I meant Q11

$\cup = \text{or}$

$\cap = \text{and}$

Sorry I'm confused on to how you would get P(AnB) without knowing the value of B?

If you combine the first formula with the second formula I gave you:

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


You know $P(A\cup B)$ and $P(A)$ so you can work out $P(B)$.