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Get Answers to all your Questions
Let two fair six-faced dice A and B be thrown simultaneously. If E1 is the event that die A shows up four, E2 is the event that die B shows up two and E3 is the event that the sum of numbers on both dice is odd, then which of the following statements is NOT true ?
Option: 1 E1 and E2 are independent.
Option: 2 E2 and E3 are independent.
Option: 3 E1 and E3 are independent.
Option: 4 E2 and E3 are independent.
Answers (1)
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E1: Die A = 4 → P(E1) = 1/6
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E2: Die B = 2 → P(E2) = 1/6
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E3: Sum is odd → P(E3) = 1/2
Now test independence using:
P(A ∩ B) = P(A) × P(B)
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E1 & E2: (4,2) → 1/36 = 1/6 × 1/6
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E2 & E3: B=2, A odd → (1,2), (3,2), (5,2) → 3/36 = 1/6 × 1/2
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E1 & E3: A=4, B odd → (4,1), (4,3), (4,5) → 3/36 = 1/6 × 1/2
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E2 & E3: Same as above
View full answer
