in a beauty pageant with 10 finalists and with equal chances of being chosen, what is the probability that contestant no. 1 will be one of the top 3 winners?
Answers
Given : in a beauty pageant with 10 finalists and with equal chances of being chosen,
To Find : the probability that contestant no. 1 will be one of the top 3 winners?
Solution:
Total Finalist = 10
3 winners out of 10 can be selected in ¹⁰C₃ ways
= 120 Ways
Let say contestant number 1 is not in top 3
Then 3 contestants out of 9 can be selected in ⁹C₃ ways
= 84 ways
Number of ways contestant number 1 in top 3 = 120 - 84 = 36 Ways
Hence probability that contestant no. 1 will be one of the top 3 winners
= 36/120
= 3/10
= 0.3
Another simpler approach :
10 contestants so probability of getting any one position = 1/10 = 0.1
Probability of getting any of 3 positions = 3 x 0.1 = 0.3
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