Question:
Four men and three women are standing in a line for railway ticket. The probability of standing them in alternate manner is
Four men and three women are standing in a line for railway ticket. The probability of standing them in alternate manner is
Updated On: Jun 20, 2022
- $\frac{1}{35}$
- $\frac{1}{33}$
- $\frac{1}{84}$
- $\frac{1}{7}$
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The Correct Option is A
Solution and Explanation
$\because$ Total outcomes $={ }^{7} P_{7}=7 !$
and favourable outcomes $=3 ! \times 4 !$
$\therefore$ Required probability $=\frac{\text { Favourable outcomes }}{\text { Total outcomes }}$
$=\frac{3 ! \times 4 !}{7 !}=\frac{3 \times 2 \times 1 \times 4 !}{7 \times 6 \times 5 \times 4 !}=\frac{1}{35}$
and favourable outcomes $=3 ! \times 4 !$
$\therefore$ Required probability $=\frac{\text { Favourable outcomes }}{\text { Total outcomes }}$
$=\frac{3 ! \times 4 !}{7 !}=\frac{3 \times 2 \times 1 \times 4 !}{7 \times 6 \times 5 \times 4 !}=\frac{1}{35}$
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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