Respuesta :
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]
The probability that both of them forgot their lunch is 1/45.
What is the combination?
A combination is a mathematical technique that determines the number of possible arrangements in a collection of items where the order of the selection does not matter.
In a class of 10, there are 2 students who forgot their lunch.
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]\rm ^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]\rm ^{10}C_2=\dfrac{10!}{(10-2)!2!} =\dfrac{10!}{8! \times 2!}= 45[/tex]
The probability that both the randomly chosen students forgot their lunch is;
[tex]\rm Probability=\dfrac{^2C_2}{^{10}C_2}=\dfrac{1}{45}[/tex]
Hence, the probability that both of them forgot their lunch is 1/45.
Learn more about combination here;
https://brainly.com/question/3447684
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