Four boys and three girls stand in a queue for an interview, the probability that they will be in alternate positions is.
By BYJU'S Exam Prep
Updated on: September 25th, 2023
Four boys and three girls stand in a queue for an interview, the probability that they will be in alternate positions is
The probability that they will be in an alternate position is 1/35. To calculate probability, you need to determine the ratio of favorable outcomes to the total number of possible outcomes.
The formula for probability is:
Probability = Number of favorable outcomes / Total number of possible outcomes
Probability is always a value between 0 and 1, where 0 represents impossibility and 1 represents certainty. It can also be expressed as a decimal, fraction, or percentage.
Table of content
What is Probability?
Probability is a measure of the likelihood or chance of an event occurring. It is expressed as a number between 0 and 1, where 0 represents an impossible event and 1 represents a certain event.
For example-
let’s consider flipping a fair coin. The probability of getting heads (H) when flipping a fair coin is 0.5, and the probability of getting tails (T) is also 0.5. This means that if you were to flip the coin many times, you would expect heads to occur approximately half the time and tails to occur the other half of the time.
Solution
we need to determine the total number of possible arrangements and the number of arrangements where the boys and girls are in alternate positions.
Total number of possible arrangements:
Since there are seven people in total (four boys and three girls), the total number of arrangements is 7!.
Number of arrangements where boys and girls are in alternate positions:
We can treat the boys as one group (B) and the girls as another group (G). The two groups can be arranged in the following ways: BGBGBGB or GBGBGBG.
For the first arrangement (BGBGBGB):
- The boys’ group (B) can be arranged in 4! ways.
- The girls’ group (G) can be arranged in 3! ways.
For the second arrangement (GBGBGBG):
- The boys’ group (B) can be arranged in 4! ways.
- The girls’ group (G) can be arranged in 3! ways.
Therefore, the total number of arrangements where the boys and girls are in alternate positions is 2 * 4! * 3!.
Now, we can calculate the probability by dividing the number of arrangements where the boys and girls are in alternate positions by the total number of possible arrangements:
Probability = (2 * 4! * 3!) / 7!
The probability of being in an alternate position is 1/35.
Summary
Four boys and three girls stand in a queue for an interview, the probability that they will be in alternate positions is
Four boys and three girls stand in a queue for an interview, the probability that they will be in alternate positions is 1/35.
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