Question

You have a 3-card deck containing a king, a queen, and a jack. You draw a random card, then without putting it back you draw a random second card from the ones that are left. Use a tree diagram to calculate the probability that you draw exactly 1 queen.

Answer 1

there is only one queen in the deck, so the probability of drawing "exactly one" queen is the same as the probability of drawing a queen

the probability you get a queen on the first draw is \(\frac{1}{3}\) and the probability you do not draw a queen and then do draw one is \(\frac{2}{3}\times \frac{1}{2}\)

Answer 2

add these up and get
\[\frac{1}{3}+\frac{1}{3}=\frac{2}{3}\]

Answer 3

it is actually easier than this.
think of the card that is left
since you have 3 cards, each on is left with probability \(\frac{1}{3}\) and so the probability that any one is selected is \(\frac{2}{3}\)

Answer 4

Thank you!