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Rufina [12.5K]
3 years ago
10

Two fair, distinct dice (one red and one green) are rolled. Let A be the event the red die comes up even and B be the event the

sum on the two dice is eight. Are A,B independent events?
Mathematics
1 answer:
forsale [732]3 years ago
7 0

Answer: No, A and B are not independent events.

Step-by-step explanation:

Since we have given that

Number of outcomes that a die comes up with = 6

A be the event that the red die comes up even.

A={2,4,6}

B be the event that the sum on the two dice is 8.

B={(2,4),(4,2),(5,3),(3,5),(44)}

P(A) = \dfrac{3}{6}=\dfrac{1}{2}

P(B) = \dfrac{5}{36}

P(A∩B) = \dfrac{3}{36}

But,

P(A).P(B) ≠ P(A∩B)

\dfrac{1}{2}\times \dfrac{5}{36}\neq \dfrac{3}{36}\\\\\dfrac{5}{72}\neq\dfrac{1}{12}

Hence, A and B are dependent events.

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