Question

What is the probability that you draw 3 cards and you selected 3 aces from a deck of 52 cards?

Answer 1

Hint: We need to calculate the probability of getting 3 aces from a deck of 52 playing cards. For this we use the probability concept. Probability can be defined as the likeliness of the occurrence of the event. It can be calculated as the number of favourable events divided by the total number of events. We consider the event of drawing 1 card followed by the next and then the third card. Using this, we can calculate the probability.

Complete step by step solution:
In order to solve this question, let us first explain the problem. Here, we are given a deck of 52 cards. We know that the number of aces in a deck of 52 cards is 4. We need to find the probability of drawing 3 cards such that all the 3 are ace cards.
Let us first pick one card. The probability for this one card being an ace is given by,
$= \dfrac{4}{52}$
This is based on the number of favourable cases, which is obtaining an ace, divided by the total number of cases which is all the cards in the deck, 52.
Next, we draw the second card from the remaining deck of 51 cards having 3 aces. The probability in this case is given by,
$= \dfrac{3}{51}$
Now, we draw the third card from the remaining cards in the deck which is 50. This contains 2 remaining aces. The probability for this is given by,
$= \dfrac{2}{50}$
Now, we find the combined probability by taking the product of the above probabilities. This is represented as,
$= \dfrac{4\times 3\times 2}{52\times 51\times 50}$
Simplifying this product by cancelling out the common factors and multiplying the remaining terms, we get
$= \dfrac{1}{5525}$
Hence, the probability that you draw 3 cards and you selected 3 aces from a deck of 52 cards is $\dfrac{1}{5525}.$

Note: We need to know the concept of probability to solve such questions. We can also solve this question by using the concept of permutations and combinations. We need to be careful while solving this problem because we need to reduce the number of cards in the deck by one after drawing one otherwise, we get a wrong answer.