Suppose a fair die has its even-numbered faces painted red. (The oddnumbered

Question

Suppose a fair die has its even-numbered faces painted red. (The oddnumbered
faces are white). Consider the experiment of rolling the die
once and the events:
A = [ 2 or 3 shows up ],
B = [ Red face shows up].
(a) Calculate P(A|B)
(b) Calculate P(A [ B). this symbol between the A and B is a union symbol that looks like a u

Answer 1

You can find the ∪ symbol here by selecting the Ω button on the menu bar. It's the first symbol in the 4th row.

 

A = {2, 3}

B = {2, 4, 6}

 

a) P(A|B) is the probability that the result satisfies A, given that B is true. There are 3 possible choices in B, 1 of which satisfies A, so

P(A|B) = 1/3

 

b) P(A ∪ B) is the probability that the result satisfies A or B. The set A ∪ B = {2, 3, 4, 6}, so

P(A ∪ B) = 4/6 = 2/3.