This question is incomplete, the complete question is;
You are in a 12-member panel. If two people from the panel are selected to represent the panel, what is the probability you wont be selected.
[ Two decimal places ]
Answer:
The probability that you be selected is 0.83
Explanation:
Given the data in the question;
total number of people in the panel = 12
number of people to be selected from the panel = 2
probability you wont be selected = ?
Number of ways of selecting 2 people from the 12 member panel is;
⇒ ¹²C₂ = 12! / ( 2!( 12 - 2 )! ) = 479001600 / 7257600 = 66
so total number of outcome = 66
Now, number of ways in favor of selecting you and another person from the 12 member panel is;
⇒ ¹C₁ × ¹¹C₁ = [1! / ( 1!( 1 - 1 )! )] × [11! / ( 1!( 11 - 1 )! )] = 1 × 11 = 11
so favorable number of outcome = 11
∴ Probability of selecting you in the panel will be;
⇒ favorable number of outcome / total number of outcome
⇒ 11 / 66 = 1/6
Now, Probability of not selecting you in the panel will be;
⇒ 1 - Probability of selecting you in the panel
⇒ 1 - 1/6
⇒ 0.83
Therefore, The probability that you be selected is 0.83