Question

Cards are dealt, one at a time, from a standard 52-card deck. a if the first 2 cards are both spades, what is the probability that the next 3 cards are also spades?

Answer 1

So we already drew two cards and both of them are spades. So that means there are 50 cards and 11 spades left.

Then third card being spades would be 11 / 50

Now there are 10 spades and 49 cards left.
So the probability for fourth card would be 10 / 49

Fifth card would be 9 / 48.

So the probability of next three cards being spades would be

`(11)/(50)\cdot(10)/(49)\cdot\frac9{48}=(33)/(3920)\approx\boxed{0.00842}`

Hope this helps.