Question

Using a Deck of Cards:

1. What is the probability of getting an Ace?

2. If in #6 you DID get an Ace, you did NOT put it back into the deck, and then you draw again, what is the probability your second card will also be an Ace?

3. If in #6 you did NOT get an Ace, you did NOT put the card back into the deck, and then you draw again, what is the probability your second card will be an Ace?

4. If in #6, you did NOT get an Ace, you did NOT put the card back into the deck, and then you draw again, what is the probability your second card will be a 7?

Answer 1

Q1) The probability of getting an ace is computed here as:
= Total number of aces / Total number of cards in the deck

= 4/52

= 1/13

Therefore 1/13 is the required probability here.

Q2) As we are putting back the ace which we obtained in the part #6, therefore the probability of getting an ace as the second card also remains the same.

Therefore 1/13 is the required probability here.

Q3) The probability that the second card is an ace given that there is a non ace card taken out is computed here as:
= Number of aces left in the deck / Number of total cards left in the deck

= 4/51

= 0.0784

Therefore 0.0784 is the required probability here.

Q4) Given that we did not get an ace as the first card, probability that the second card will be a 7 is computed here as:
= (1 - Probability that the second card is an ace) / 12

This is because all the cards except Ace are equally likely when Ace is not getting selected as the second card

= (1 - 0.0784) / 12

= 0.0768

Therefore 0.0768 is the required probability here.