Question

A deck of cards has 3 blue, 4 black, and 6 purple cards. Draw 2 cards without replacing any cards. What is the probability of both cards being blue?

Answer 1

To solve this question, simply add up the total number of cards in the pile

This is 11 cards remove 2 so this is 9.

The probability of 1 card being blue is 3/9 or 1/3.

Both would be (1/3)^2 which is 1/9.

Answer 2

1/26

The probability of the first card being blue is 3/13, black is 4/13, and purple is 6/13. Presuming that the first card will be blue, and is then removed, then the odds now stand at 2/12 for blue (there is one less blue, and one less card, so both numbers decrease), 4/12 for black (the number of black remains the same but a different card has been removed, so only the bottom number changes) and 6/12 for purple (explanation as with black).
So, the odds are 3/13 and 2/12 that both cards will be blue. Multiplying these together gives your final answer of 3/78, or 1/26!

Hope this helped you! It was hard to explain, so if you need clarification, just say.