Question

20. Three cards are selected form a standard deck of cards and not

replaced. What is the probability that all three are diamonds? Give your
answer as a fraction or a decimal rounded to 4 places.
Your answer

Answer 1

We have a probability of
`(13)/(52)=(1)/(4)` for the first card to be a diamond. Having drawn this first card without replacement, there are now 12 diamonds remaining in a deck of 51 cards, so the probability that the second card is a diamond, given that the first card was a diamond, is
`(12)/(51)=(4)/(17).` Similarly, for the third card, there are 11 diamonds in a deck of 50, so the probability of drawing a third diamond is
`(11)/(50).` Now, since these events are dependent, we multiply these three probabilities to get our answer of
`(11)/(850).`