In the beauty pageant with 10 finalist and with equal chances of neing chosen. What is the probability that contestant no. 1 will be one the top 2 winner?
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 2winners?
Solution:
Total Finalist = 10
2 winners out of 10 can be selected in ¹⁰C₂ ways
= 45 Ways
Let say contestant number 1 is not in top 2
Then 2 contestants out of 9 can be selected in ⁹C₂ ways
= 36 ways
Number of ways contestant number 1 in top 2 =45 - 36 = 9 Ways
Hence probability that contestant no. 1 will be one of the top2 winners
= 9/45
= 1/5
= 0.2
Another simpler approach :
10 contestants so probability of getting any one position = 1/10 = 0.1
Probability of getting any of 2 positions = 2 x 0.1 = 0.2
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