Question

Say you're playing three-card poker; that is, you're dealt three cards in a row at random from a standard deck of 52 cards. What are the odds of getting a pair or three of a kind?

Answer 1

Answer:

Step-by-step explanation:

Given

There are 52 cards in total

there are total of 13 pairs of same cards with each pair containing 4 cards

Probability of getting a pair or three of kind card=1-Probability of all three cards being different

Probability of selecting all three different cards can be find out by selecting a card from first 13 pairs and remaining 2 cards from remaining 12 pairs i.e.

$=\frac{52\times 48\times 44}{52\times 51\times 50}$

for first card there are 52 options after choosing first card one pair is destroyed as we have to select different card .

For second card we have to select from remaining 12 pairs i.e. 48 cards and so on for third card.

Required Probability is $=1-\frac{52\times 48\times 44}{52\times 51\times 50}$

$=\frac{22776}{132600}$