A group of 20 students contains 10 who believe Anna is doing a good job, 5...

A group of 20 students contains 10 who believe Anna is doing a good job, 5 who believe Anna is doing a bad job and 5 who do not know who Anna is. Two students are chosen at random. What are the probabilities? Both do not know who Anna is One believes Anna is doing a good job and 1 who believes Trump is doing a poor job

Expert Solution

Number of ways to select two students from a group of 20 students = ²⁰C₂ = 20! / ((20-2)! 2!) = (20 * 19)/2 = 190

Number of ways to select two students who do not know who Anna is = ⁵C₂ = 5! / ((5-2)! 2!) = (5 * 4)/2 = 10

Probability that both students do not know who Anna = Number of ways to select two students who do not know who Anna is / Number of ways to select two students from a group of 20 students

= 10 / 190 = 1/19

Number of ways to select two students in which one believes Anna is doing a good job and 1 who believes Anna is doing a poor job = ¹⁰C₁ * ⁵C₁ = 10 * 5 = 50

Probability that one believes Anna is doing a good job and 1 who believes Anna is doing a poor job = Number of ways to select two students in which one believes Anna is doing a good job and 1 who believes Anna is doing a poor job / Number of ways to select two students from a group of 20 students

= 50 / 190

= 5 / 19

orchestra answered 2 years ago

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