Question

1. Bill spins two spinners that have 3 equal sections numbered 1 through 3. If he spins a 2 on at least one spin, what is the probability that the sum of his two spins is an odd number? [Hint: think of ALL possible combinations that could happen using the two spinners as described above]

2. Each letter of the alphabet is written on a card using a red ink pen and placed in a container. Each letter of the alphabet is also written on a card using a black ink pen and placed in the same container. A single card is drawn at random from the container of 52 total letters. What is the probability that the card drawn has a letter written in red ink, the letter Q, or the letter P?

Answer 1

We would be looking at the first question here as:

Q1) For the two spins, the distribution here is given as:

P(11) = P(12) = P(13) = P(21) = P(22) = P(23) = P(31) = P(32) = P(33) = 1/9

as each combination is equally likely.

The probability that the sum of his two spins is an odd number given that he spins a 2 on at least one spin is computed here using Bayes theorem as:

= number of combinations where there is at least one 2 and sum is odd / number of combinations with at least one 2.

= P( 21, 23, 12, 32) / P( 12, 21, 22, 23, 32)

= 4/5

= 0.8

Therefore 0.8 is the required conditional probability here.