In a class of 10, there are 2 students who forgot their lunch.If the teacher chooses 2 students, what is the probability that both of them forgot their lunch?
Accepted Solution
A:
Answer: The required probability is [tex]\dfrac{1}{45}.[/tex]Step-by-step explanation: Given that in a class of 10, there are 2 students who forgot their lunch.If the teacher chooses 2 students, we are to find the probability that both of them forgot their lunch.Since there are two students who forgot their lunch, so the number of ways in which 2 students can be chosen from 2 students is given by [tex]^2C_2=\dfrac{2!}{2!(2-2)!}=1.[/tex]The number of ways in which 2 students can be chosen from 10 students is given by[tex]^{10}C_2=\dfrac{10!}{2!(10-2)!}=\dfrac{10\times 9\times 8!}{2\times 1\times 8!}=5\times 9=45.[/tex]Therefore, the probability that both the randomly chosen students forgot their lunch is[tex]P=\dfrac{^2C_2}{^{10}C_2}=\dfrac{1}{45}.[/tex]Thus, the required probability is [tex]\dfrac{1}{45}.[/tex]