Tamil Nadu Board of Secondary EducationSSLC (English Medium) Class 10th

# If A, B, C are any three events such that probability of B is twice as that of probability of A and probability of C is thrice as that of probability of A and if P(A ∩ B) = 16, P(B ∩ C) = 14, P(A ∩ - Mathematics

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If A, B, C are any three events such that probability of B is twice as that of probability of A and probability of C is thrice as that of probability of A and if P(A ∩ B) = 1/6, P(B ∩ C) = 1/4, P(A ∩ C) = 1/8, P(A ∪ B ∪ C) = 9/10 and P(A ∩ B ∩ C) = 1/15, then find P(A), P(B) and P(C)

#### Solution

By the given condition,

P(B) = 2P(A), P(C) = 3P(A)

P(A ∪ B ∪ C) = P(A) + P(B) + P(C) – P(A ∩ B) – P(B ∩ C) – P(A ∩ C) + P(A ∩ B ∩ C)

9/10 = "P"("A") + 2"P"("A") + 3"P"("A") - 1/6 - 1/4 - 1/8 + 1/15

9/10 = 6"P"("A") - 1/6 - 1/4 - 1/8 + 1/15

6P(A) = 9/10 + 1/6 + 1/4 + 1/8 - 1/15

= (108 + 20 + 30 + 15 - 8)/120

= (173 - 8)/120

= 165/120

= 33/24

= 11/8

6P(A) = 11/8

⇒ P(A) = 11/(6 xx 8)

P(A) = 11/48

P(B) = 2 × P(A)

P(B) = 2 xx 11/48 = 11/24

P(C) = 3P(A)

= 3 xx 11/48 = 11/6

P(A) = 11/48, P(B) = 11/24, P(C) = 11/16

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#### APPEARS IN

Samacheer Kalvi Mathematics Class 10 SSLC Tamil Nadu State Board
Chapter 8 Statistics and Probability
Exercise 8.4 | Q 13 | Page 330