Question:
For a party $8$ guests are invited by a husband and his wife. They sit in a row for dinner. The probability that the husband and his wife sit together is
For a party $8$ guests are invited by a husband and his wife. They sit in a row for dinner. The probability that the husband and his wife sit together is
Updated On: Sep 3, 2024
- $ \frac{2}{7} $
- $ \frac{2}{9} $
- $ \frac{1}{9} $
- $ \frac{4}{9} $
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The Correct Option is B
Solution and Explanation
Total number of way of sitting $=9 !$
and number of favourable ways of sitting $=2 \times 8 !$
$\therefore$ Required probability $=\frac{2 \times 8 !}{9 !}=\frac{2}{9}$.
and number of favourable ways of sitting $=2 \times 8 !$
$\therefore$ Required probability $=\frac{2 \times 8 !}{9 !}=\frac{2}{9}$.
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Concepts Used:
Event
A probability event can be defined as a set of outcomes of an experiment. In other words, an event in probability is the subset of the respective sample space. The likelihood of occurrence of an event is known as probability. The probability of occurrence of any event lies between 0 and 1.
Thus, an event is a subset of the sample space, i.e., E is a subset of S.
There could be a lot of events associated with a given sample space. For any event to occur, the outcome of the experiment must be an element of the set of event E.
Probability of Occurrence of an Event
P(E) = Number of Favourable Outcomes/ Total Number of Outcomes
Types of Events in Probability:
Some of the important probability events are:
- Impossible and Sure Events
- Simple Events
- Compound Events
- Independent and Dependent Events
- Mutually Exclusive Events
- Exhaustive Events
- Complementary Events
- Events Associated with “OR”
- Events Associated with “AND”
- Event E1 but not E2