A die is tossed thrice. Find the probability of getting an odd number at least once.
Solution and Explanation
Probability of getting an odd number in a single throw of a die=\(\frac{3}{6}=\frac{1}{2}\)
Similarly,probability of getting an even number \(=\frac{3}{6}=\frac{1}{2}\)
Probability of getting an even number three times\(=\frac{1}{2}\times \frac{1}{2}\times \frac{1}{2}=\frac{1}{8}\)
Therefore, probability of getting an odd number at least once
=1-Probability of getting an odd number in none of the throws
=1-Probability of getting an even number thrice
\(=1-\frac{1}{8}\)
\(=\frac{7}{8}\)
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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