Respuesta :
Answer: [tex]\frac{6_C_2}{20_C_2}[/tex]
Step-by-step explanation:
According to the question total sophomores = 6
Total freshmen = 14
Therefore, total persons = 6+ 14 = 20
Thus, If two person are chosen the probability that both are sophomores,
P = Total combination of 2 person from the group of 6 sophomores/ total persons
P = [tex]\frac{6_C_2}{20_C_2}[/tex], which is the required expression.
Note: we can further solve the value of P as follow,
⇒P= [tex]\frac{6!/4!2!}{20!/18!2!}[/tex]
⇒P=[tex]\frac{30/2}{10\times 19}[/tex]
⇒P=[tex]\frac{15}{190}[/tex]
The expression (6_P_1)(5_P_1)/(20_P_2) represents the probability that both students chosen are sophomores if the six sophomores and 14 freshmen are competing for two alternate positions on the debate team.
What is probability?
It is defined as the ratio of the number of favorable outcomes to the total number of outcomes, in other words the probability is the number that shows the happening of the event.
We have:
Number of sophomores = 6
Number of freshmen = 14
Total = 20
And these two are competing for two alternate positions on the debate team.
Two students can be arranged out of 6 = [tex]\rm _{6}^{}\textrm{P}_1\times _{5}^{}\textrm{P}_1[/tex]
Total arrangements with 20 students = [tex]_{20}^{}\textrm{P}_2[/tex]
Now the probability:
[tex]= \frac{\rm _{6}^{}\textrm{P}_1\times _{5}^{}\textrm{P}_1}{_{20}^{}\textrm{P}_2}[/tex]
Thus, the expression (6_P_1)(5_P_1)/(20_P_2) represents the probability that both students chosen are sophomores if the six sophomores and 14 freshmen are competing for two alternate positions on the debate team.
Learn more about the probability here:
brainly.com/question/11234923
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