What is the probability that a number selected at random from the number $ 1, 2,2,3,3,3,4,4,4,4 $ will be their average?
Given:
Numbers \( 1, 2,2,3,3,3,4,4,4,4 \) are given.
To do:
We have to find the probability that a number selected at random from the number \( 1, 2,2,3,3,3,4,4,4,4 \) will be their average.
Solution:
Numbers \( 1, 2,2,3,3,3,4,4,4,4 \) are given.
This implies,
The total number of numbers $=1+2+3+4=10$
The total number of possible outcomes $n=10$.
Average of the given numbers $=\frac{1+2+2+3+3+3+4+4+4+4}{10}=\frac{30}{10}=3$
Total number of favourable outcomes(the number selected being equal to average) $=3$.
We know that,
Probability of an event $=\frac{Number\ of\ favourable\ outcomes}{Total\ number\ of\ possible\ outcomes}$
Therefore,
Probability that the number selected is equal to average $=\frac{3}{10}$
The probability that a number selected at random from the number \( 1, 2,2,3,3,3,4,4,4,4 \) will be their average is $\frac{3}{10}$.
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