Question

Suppose there are three cards in a deck: one marked with a 1, one marked with a 2, and one marked with a 5. You draw two cards at random and without replacement from the deck of three cards. The sample space S = {(1,2), (2,1),(1,5),(5,1),(2,5),(5,2)} consists of these six equally likely outcomes. Let X be the total of the two cards drawn. What would be the probabilities for X?

Answer 1

`P(x=7) = 1/3\\P(x=6) = 1/3\\P(X=3) = 1/3`

Explanation:

Given that there are three cards in a deck: one marked with a 1, one marked with a 2, and one marked with a 5

You draw two cards at random and without replacement from the deck of three cards. The sample space S = {(1,2), (2,1),(1,5),(5,1),(2,5),(5,2)} consists of these six equally likely outcomes

X = total of two cards can take values as

X 3 6 7

P 1/3 1/3 1/3

i.e. probability distribution for sum is

`P(x=7) = 1/3\\P(x=6) = 1/3\\P(X=3) = 1/3`