two card are chosen at random from a standard deck of cards with replacement. What is the probabilit of getting two aces
if there are no jokers, it is 1 out of 13. if there are jokers, it is one out of fourteen
Lorraine is NOT correct
My answer is 1/221 or 1 out of 221. Why? Since there are 4 aces in a deck of card (52). it is written as 4/52 simplified to 1/13. Then find the prob. for the next one is 3/51 because you had take away 1, you have to subtract it from both the 4 aces and the deck( 52-1=51) Therefore you multiplied both of them to find the prob. because they are independent events; 1/13 x 3/51= 3/663 simplified by 3 and get 1/221
To find the probability of getting two aces from a standard deck of cards with replacement, we can break down the problem into two parts:
1) Finding the probability of drawing the first ace.
2) Finding the probability of drawing the second ace, given that the first card drawn was an ace (since replacement is allowed).
Let's go through the calculation step by step:
1) There are a total of 52 cards in a standard deck, and 4 of them are aces. Therefore, the probability of drawing the first ace is:
P(Drawing First Ace) = Number of Aces / Total Number of Cards
= 4 / 52
= 1 / 13
2) Since replacement is allowed, after drawing the first ace, we put it back in the deck and shuffle, so now we have a total of 52 cards to choose from again, including 4 aces.
Therefore, the probability of drawing the second ace, given that the first card drawn was an ace, is:
P(Drawing Second Ace | First Ace) = Number of Aces / Total Number of Cards
= 4 / 52
= 1 / 13
Now, to find the probability of both events occurring (drawing two aces in a row), we multiply the probabilities:
P(Drawing Two Aces) = P(Drawing First Ace) * P(Drawing Second Ace | First Ace)
= (1/13) * (1/13)
= 1/169
So, the probability of getting two aces from a standard deck of cards with replacement is 1/169.