Can anyone help me

Question

Find p(a and b) if p(a) = 0.8 p(a|b)=0.3 and p(b|a) =0.1 

Answer 1

draw a Venn diagram, with 2 overlapping circles or use Bayes Theorem

pa = .8, p(a/b) = .3, p(b/a) = .1

P(a/b)p(b) = p(b/a)p(a)

.3p(b) = .1(.8) = .08

p(b) = .08/.3 = 8/30

p(a)+p(b) = 8/10 + 8/30 = 32/30 = 16/15

p(aUb) = p(a) +p(b) - p(a^b) = 16/15 - 1/15= 1, if p(~a v ~b)=0