If A and B are two independent events such that =2/15 and =1/6, then find P(B).

Let , denote the complements of A, B respectively.

Given that, P(A∩) )

P(A)P()

P(A)[1–P(B)]

P(A)=1/6[1–P(B)]

P(A'∩B)

P(A')P(B)

[1–P(A)]P(B) )

[1–1/6{1–P(B)}]P(B) )

[{6–6P(B)–1}/{6–6P(B)}]P(B) )

15[5–6P(B)]P(B)=2[6–6P(B)]

15[5–6P(B)]P(B)=12[1–P(B)]

5[5–6P(B)]P(B)=4[1–P(B)]

25P(B)–30[P(B)]²=4–4P(B)

–30[P(B)]²+25P(B)+4P(B)–4=0

30[P(B)]²–29P(B)+4=0

30a²–29a+4=0 where P(B)=a

30a²–24a–5a+4=0

6a(5a–4)–1(5a–4)=0

(6a–1)(5a–4)=0

6a–1=0

6a=1

a

P(B)

5a–4=0

5a=4

a=

P(B)

Therefore, P(B),