Math - probability

Question

ten cards are marked with letters P, R,O, P, O, R T, I, O, N respectively. Three cards are placed in a box. A card is drawn from the box. What is the probability that the card bears the letter 'O'.

Answer 1

In this problem all that is essential is that there are 3 o's and 7 "not o's".

Let D = ₁₀C₃, then number of ways of picking 3 things from 10. This is the denominator in the hypergeometric distribution.

There are ₇C_3-k * ₃C_k ways of picking k o's and 3-k "not o's" from a group of 10...and in in this case we are not interested in k=0. Call this number N_k.

The probability of an o from a group 3 containing 1 o is 1/3, 2 o's 2/3 and 3 o's 1.

Therefore the probability you seek is the sum of (k/3)*N_k/D for k=1 to 3.

Answer 2

Three O's out of 10 cards.

3 / 10