Conditional Probability

  • #1

Main Question or Discussion Point

I could have posted this in the homework section but I didn't see a section on probability. Also, this is more of a general conditional probability question asked through an example.



A band called Radiohead is inspired by an old band called The Beatles.
50% of music critics think the beatles was a great (G) band, 40% that it
was moderate (M) and 10% that it was awful (A). These critics have also
compiled the following table:


0.8 0.1 0.1
0.1 0.9 0
0.2 0.3 0.5


The table says that the probability of a new band (B2) being great given
that the inspiring band (B1) was great is P (B2 = GjB1 = G) = 0:8: Similarly, P (B2 = GjB1 = M) = 0:1, P (B2 = MjB1 = A) = 0:3, and so on.
Note that the numbers in the rows add up to 1, so the table is a probability
transition matrix.
1. Given what the critics think of the Beatles and the fact that the Beatles
inspired Radiohead, what is the probability that Radiohead is a great
band?
2. What is P (B1 = GjB2 = G)?




For 1 I get 0.50*0.8 + 0.40*0.1 + 0.10*0.2 = 0.46 which I think is correct.


However, I am having trouble with part 2. I can write

P(B1 = G | B2 = G) = P(B2 = G | B1 = G)P(B1 = G) / P(B2 = G)

which leads to 0.8 * P(B1 = G) / P(B2 = G)

I also notice that P(B2 = G) = 1 cause we are told.

This leads to

P(B1 = G | B2 = G) = 0.8*P(B1 = G)

Is there any way to get an exact answer for this? Or do I have to find a different way to tackle this problem?
 

Answers and Replies

  • #2
EnumaElish
Science Advisor
Homework Helper
2,304
124
"Given A" does not mean "assume P(A) = 1." Use your answer in part 1.
 

Related Threads on Conditional Probability

Replies
4
Views
371
  • Last Post
Replies
2
Views
680
  • Last Post
Replies
3
Views
172
  • Last Post
Replies
1
Views
1K
  • Last Post
Replies
3
Views
630
  • Last Post
Replies
2
Views
1K
  • Last Post
Replies
1
Views
997
Replies
3
Views
529
  • Last Post
Replies
7
Views
2K
  • Last Post
Replies
1
Views
2K
Top