Question:
The probability of obtaining an even prime number on each die when a pair of dice is rolled is:
The probability of obtaining an even prime number on each die when a pair of dice is rolled is:
Updated On: Jan 18, 2024
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\((\frac{1}{3})\)
\((\frac{1}{12})\)
\((\frac{1}{36})\)
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The Correct Option is D
Solution and Explanation
The correct answer is D:\(\frac{1}{36}\)
When two dice are rolled, the number of outcomes is 36.
The only even prime number is 2.
Let E be the event of getting an even prime number on each die.
∴E={2,2}
\(P(E)=\frac{1}{36}\)
Hence option (D) is correct.
When two dice are rolled, the number of outcomes is 36.
The only even prime number is 2.
Let E be the event of getting an even prime number on each die.
∴E={2,2}
\(P(E)=\frac{1}{36}\)
Hence option (D) is correct.
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Concepts Used:
Multiplication Theorem on Probability
In accordance with the multiplication rule of probability, the probability of happening of both the events A and B is equal to the product of the probability of B occurring and the conditional probability that event A happens given that event B occurs.
Let's assume, If A and B are dependent events, then the probability of both events occurring at the same time is given by:
\(P(A\cap B) = P(B).P(A|B)\)
Let's assume, If A and B are two independent events in an experiment, then the probability of both events occurring at the same time is given by:
\(P(A \cap B) = P(A).P(B)\)
Read More: Multiplication Theorem on Probability