You apply to 20 graduate programs 10 of which are in clinica

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 front (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.

Solution

P(the letter is from clinical psychology program) = 10/20 = 0.5

There are 10 programs in clinical psychology out of 20. Therefore the chances of getting a letter for one of the clinical program will be (10/20)

b.) P( a counseling psychology program)

= 5/20 = 0.25

There are 5 counseling psychology program so the chances for getting a letter for one of these programs from the 20 programs will be (5/20)

c.) P( from any program other than social work)

= 15/20 = 0.75

There are 15 other programs other than social work so the chances of getting a letter for one of the 15 programs from 20 programs is (15/20)