The following Venn diagram shows the events A and B , where P(A)=0.4, P(A ∪ B) = 0.8 and P(A ∩ B) = 0.1. The values p and q are probabilities.

Question

(i) Write down the value of q

(ii) Find the value of p

Find P(B)

Answer 1

P(A ∪ B) = P(A) + P(B) - P(A ∩ B)

where P(A)=0.4, P(A ∪ B) = 0.8 and P(A ∩ B) = 0.1.

 

P(A ∪ B) = P(A) + P(B) - P(A ∩ B)

 

.8          =  .4    + P(B) - .1

 

.8-.4+.1 =            P(B)

.5          =            P(B)

 

Tiffany, missing some context with regards to 

(i) Write down the value of q
(ii) Find the value of p

 

generally p + q = 1;  p = 1-q and q = 1-p

 

Cheers