# Solve the following: If P(A) = P(AB)=15,P(BA)=13 the find P(BA) - Mathematics and Statistics

Sum

Solve the following:

If P(A) = "P"("A"/"B") = 1/5, "P"("B"/"A") = 1/3 the find "P"("B"/"A")

#### Solution

It is given that, P(A) = "P"("A"/"B") = 1/5

"P"("B"/"A") = 1/3

Now P(A ∩ B) = "P"("A")*"P"("B"/"A") = 1/5*1/3 = 1/15

Also, P(A ∩ B) = "P"("B")*"P"("A"/"B")

∴ 1/15 = "P"("B")*1/5

∴ P(B) = 1/3

∴ P(A)·P(B) = 1/5*1/3 = 1/15 = P(A ∩ B)

∴ A, B are independent

∴ A', B; A', B' are also independent

"P"("B'"/"A'") = ("P"("B'" ∩ "A'"))/("P"("A'"))

= ("P"("B'")*"P"("A'"))/("P"("A'"))   ...[∵ A' and B' are independent]

= 1 – P(B)

= 1 - 1/3

= 2/3

Concept: Independent Events
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#### APPEARS IN

Balbharati Mathematics and Statistics 1 (Arts and Science) 11th Standard Maharashtra State Board
Chapter 9 Probability
Miscellaneous Exercise 9 | Q II. (11) (ii) | Page 214