You apply to 20 graduate programs, 10 of which are in clinical psychology, 5 of which are in counseling psychology, and 5 of which are in social work. You get a message from home that you have a letter from one of the programs you applied to, but nothing is said about which one. Give the probabilities it is from (a) a clinical psychology program, (b) a counseling psychology program, (c) from any program other than social work. (d) Explain your answers to someone who has never had a course in statistics.

[tex]%[/tex]Answer:a) The probabilities for a message coming from the clinical psychology program are: [tex]\frac{10}{20} =\frac{1}{2}=50percent[/tex]b) The probabilities for a message coming from the counseling program are: [tex]\frac{5}{20} =\frac{1}{4}=25percent[/tex]c) The probabilities for a message coming from the social work program are: [tex]\frac{5}{20} =\frac{1}{4}=25percent[/tex]Step-by-step explanation:Probabilities are used to calculate the possibility that exist for a thing to happen at random. An easy way to calculate then is by dividing the chances of one of the things to happen by the total of things. These answers can be given in percentage.In this case the total of things are the 20 graduate programs and each one of the things are 10 of clinical psychology, 5 of counseling psychology, and 5 of social work.So now the probabilities for a message coming from the clinical psychology program are: [tex]\frac{10}{20} =\frac{1}{2}=50percent[/tex] (a)The probabilities for a message coming from the counseling program are: [tex]\frac{5}{20} =\frac{1}{4}=25percent[/tex] (b)The probabilities for a message coming other than from the social work program are: [tex]\frac{10}{20}+\frac{5}{20} =\frac{15}{20}=75percent[/tex] (c)