Probability of choosing an employee

[vishnu rajesh]

In a company of 100 employees, including Alice and Bob, 40 were selected randomly. What is the probability that both of them are selected among the 40 members?

Thanks in advance

 

[pka]

In a company of 100 employees, including Alice and Bob, 40 were selected randomly. What is the probability that both of them are selected among the 40 members?

There are \(\displaystyle \dbinom{98}{38}=2166073259338624842623949168\) ways to include Alice & Bob: SEE HERE.

 

[vishnu rajesh]

Thank you very much. Can you explain how did you conclude?

I thought (1/100)*(1/99)*40C2 is the solution

 

[pka]

Thank you very much. Can you explain how did you conclude?
I thought (1/100)*(1/99)*40C2 is the solution

Go HERE. Study the calculations.
This probability is simple: the number of ways you want divided by the total number of ways possible.

 

[Steven G]

I always like to think hypergeometric.
Think of the 100 employees in two groups. One group having two members (Alice and Bob) and the other group having 98 members. Know you want to pick 40 from the 100 which includes Alice and Bob. So you want to choose 2 from the group of 2 employees. AND the remaining 38 from the group of 98 employees. This can be done in ₂C₂*₉₈C₃₈ ways.