Two cards are selected, without replacing the first card, from a standard deck. Find the probability of selecting an ace (A), and then selecting a 4 (B): (choose 2)
0.603%
0.592
0.592%
They are dependent events.
0.00592
To find the probability of selecting an ace (A) and then selecting a 4 (B), we need to consider the total number of possible outcomes and the number of favorable outcomes.
Step 1: Total number of possible outcomes:
When two cards are selected without replacement from a standard deck of 52 cards, the total number of possible outcomes can be calculated using the combination formula:
nCr = n! / r!(n-r)!
Here, n is the total number of cards in the deck (52) and r is the number of cards being selected (2) without replacement.
nCr = 52! / 2!(52-2)!
= 52! / 2! x 50!
= (52 x 51 x 50!) / (2 x 1 x (50 x 49 x 48!))
= (52 x 51) / 2
= 1326
Therefore, there are 1326 possible outcomes.
Step 2: Number of favorable outcomes:
We want to find the probability of selecting an ace (A) and then selecting a 4 (B).
Number of favorable outcomes for selecting an ace (A):
Since there are 4 aces in a deck, the number of favorable outcomes for selecting an ace (A) is 4.
Number of favorable outcomes for selecting a 4 (B):
Since there are 4 cards with a value of 4 (one each in the four suits), the number of favorable outcomes for selecting a 4 (B) is 4.
To find the total number of favorable outcomes for the combined event (A and B), we multiply the number of favorable outcomes for selecting an ace (A) and selecting a 4 (B):
Number of favorable outcomes = 4 x 4 = 16
Step 3: Calculate the probability:
The probability of an event is given by the formula:
Probability = Number of favorable outcomes / Total number of possible outcomes
Probability = 16 / 1326 ≈ 0.01207
Therefore, the probability of selecting an ace (A) and then selecting a 4 (B) is approximately 0.01207, which is equivalent to 1.207%.
To find the probability of selecting an ace and then selecting a 4, we need to consider the total number of possible outcomes and the number of favorable outcomes.
First, let's determine the total number of possible outcomes. A standard deck of playing cards consists of 52 cards.
For the first card selection (event A), there are 4 aces in the deck. So, the probability of selecting an ace as the first card is 4/52.
After the first card selection, we don't replace the card back into the deck. Therefore, for the second card selection (event B), the deck now contains 51 cards.
Out of the remaining 51 cards, there are 4 cards with a value of 4. So, the probability of selecting a 4 as the second card, given that we selected an ace as the first card, is 4/51.
To find the probability of both events A and B occurring, we multiply the probabilities of each event:
P(A and B) = P(A) * P(B|A)
P(A and B) = (4/52) * (4/51)
P(A and B) = (1/13) * (4/51)
P(A and B) = 4/663
Converting this to a percentage, we get:
P(A and B) ≈ 0.603%
Therefore, the correct answer is approximately 0.603%.
4/52 * 4/51 = 0.00603
so, knowing that, choose 2