Q. 85.0( 1 Vote )

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

Answer :

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),


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