Maharashtra State BoardHSC Science (Electronics) 11th
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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")`

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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
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