Discuss the following problem:
Q1. A mini license plate for a toy car must consist of a number followed by two letters. Each letter must be a C, A or R. Each number must be a 3 or 7. Repetition of letters is permitted.
Use the counting principle to determine the number of points in the sample space.
Construct a tree diagram to represent this situation
List the sample space.
Determine the exact probability of creating a mini license plate with a C. Give solution exactly in reduced fraction form.
Q2. Given that P(A) = 0.6 and P(B) = 0.3, and P(A and B) = 0.18, determine P(B|A).
a. 0.20
b. 0.30
c. 0.72
d. 0.60
Q3. Each of the numbers 0 through 30 is written on a piece of paper and all of the pieces of paper are placed in a hat. One number is selected at random. Determine the probability that the number selected is even.
a. 16/31
b. 1/2
c. 8/15
d. 15/31
Q4. Consider the Venn diagram below. The numbers in the regions of the circle indicate the number of items that belong to that region.
Determine
n(A)
n(B)
P(A)
P(B)
P(A|B)
P(B|A).