Question

a) Suppose that there is a 6-sided die that is weighted in such a way that each time the die is rolled, the probabilities of rolling any of the numbers from 1 to 5 are all equal, but the probability of rolling a 6 is twice the probability of rolling a 1. When you roll the die once, the 6 outcomes are not equally likely. What are the probabilities of the 6 outcomes? b) The probability that a manager reads the Daily Telegraph is 0.7. The probability that she reads the Daily Telegraph but not the Financial Times is 0.6. The probability that she reads neither is 0.2. Find the probability that she reads the Financial Times only.

Answer 1

(a) Let X denote the outcome when rolling the dice

Given: P(X = 6) = 2P(X = 1)

P(X = 1) = P(X = 2) = P(X = 3) = P(X = 4) = P(X = 5)

We should have,

P(X = 1) = 1/7, P(X = 6) = 2/7

X	1	2	3	4	5	6
P(X = x)	1/7	1/7	1/7	1/7	1/7	2/7

(b) Let D and F denote the events that the manager reads Daily Telegraph and Financial Times respectively

P(D) = 0.7

P(D and F') = 0.6

P(D' and F') = 0.2

The probability that she reads the Financial Times only

= P(F and D')

Now, P(D') = P(D' and F) + P(D' and F')

-> 0.3 = P(D' and F) + 0.2

-> P(D' and F) = 0.1