SOLUTION: When a card is selected from a standard deck of cards, find the probability of getting an ace followed by an ace without replacement

Click here to see ALL problems on Probability-and-statistics

Question 228239: When a card is selected from a standard deck of cards, find the probability of getting an ace followed by an ace without replacement
Found 2 solutions by drj, Edwin McCravy:
Answer by drj(1380) (Show Source):
You can put this solution on YOUR website!
When a card is selected from a standard deck of cards, find the probability of getting an ace followed by an ace without replacement

Step 1. We note that there are 4 aces in a 52-card deck.

Step 2. The probability of an ace in the first card is we call this the P(A)

Step 3. Since there is no replacement, there are only 3 aces out of the 51 cards since we assume an ace is drawn in the first card. Therefore, the probability of an ace on the second draw is P(B|A)=. We call this P(B|A) where the Probability of drawing an Ace on the second draw given that Probability of A occurred or an ace was drawn on the first try. This is also known as a conditional probability.

Step 4. The probability is the product of the probabilities found in Steps 2 and 3. P(A and B)=P(B|A)P(A) or P(A and B)=

Step 5. ANSWER: The probability of getting an ace followed by an ace without replacement is

I hope the above steps were helpful.

For FREE Step-By-Step videos in Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra and for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry.

Good luck in your studies!

Respectfully,
Dr J

Answer by Edwin McCravy(20056) (Show Source):
You can put this solution on YOUR website!
When a card is selected from a standard deck of cards, find the probability of getting an ace followed by an ace without replacement

P[getting an ace out of 52-card deck with 4 aces] times P[getting an ace out of a 51-card deck with 3 aces] = x = x= Edwin