-Three cards are drawn from a standard deck of cards without replacement. what is the probability that all three cards will be clubs
f. 3/4
g. 11/850
h. 1/3
i. 36/153
please help....!!!!!
First card: 13 cards out of 52
second card: 12 cards out of 51
third card: 11 cards out of 50
Probability of all three happening:
(13/52)(12/51)(11/50)=?
11/850
To find the probability of drawing three clubs without replacement from a standard deck of cards, we need to determine the number of favorable outcomes (drawing three clubs) and divide it by the total number of possible outcomes.
First, let's determine the number of favorable outcomes:
There are 13 clubs in a standard deck of 52 cards.
When you draw the first card, there are 13 clubs out of 52 cards to choose from.
After drawing the first club, there are 12 clubs left out of 51 cards.
Finally, after drawing the second club, there are 11 clubs left out of 50 cards.
Therefore, the total number of favorable outcomes is: 13/52 * 12/51 * 11/50 = 0.03921568627
Next, let's determine the total number of possible outcomes:
When you draw the first card, there are 52 cards to choose from.
After drawing the first card, there are 51 cards left.
Finally, after drawing the second card, there are 50 cards left.
Therefore, the total number of possible outcomes is: 52/52 * 51/51 * 50/50 = 1
Now, we can calculate the probability by dividing the number of favorable outcomes by the total number of possible outcomes:
Probability = Number of favorable outcomes / Total number of possible outcomes
Probability = 0.03921568627 / 1 = 0.03921568627
So, the probability of drawing three cards that are all clubs is approximately 0.0392.
None of the options provided (f. 3/4, g. 11/850, h. 1/3, i. 36/153) are correct. The correct answer is not listed among the options.
To find the probability that all three cards drawn will be clubs, we need to determine the number of favorable outcomes (drawing three clubs) and divide it by the total number of possible outcomes when drawing three cards from a standard deck without replacement.
Step 1: Determine the number of favorable outcomes.
In a standard deck of 52 cards, there are 13 clubs. When drawing three cards without replacement, we want all three to be clubs. The number of favorable outcomes is calculated as:
Number of favorable outcomes = (Number of ways to choose 3 clubs) = C(13, 3) = 13! / (3!(13-3)!) = 286
Step 2: Determine the total number of possible outcomes.
When drawing three cards without replacement, the total number of possible outcomes is calculated as:
Total number of possible outcomes = (Number of ways to choose 3 cards from 52) = C(52, 3) = 52! / (3!(52-3)!) = 22100
Step 3: Calculate the probability.
To calculate the probability, divide the number of favorable outcomes by the total number of possible outcomes:
Probability = Number of favorable outcomes / Total number of possible outcomes
Probability = 286 / 22100 ≈ 0.01295
Now, let's compare this result to the answer options provided:
f. 3/4 ≈ 0.75
g. 11/850 ≈ 0.01294
h. 1/3 ≈ 0.33333
i. 36/153 ≈ 0.23529
Among the given options, g. 11/850 is the closest approximation to the calculated probability of 0.01295. Therefore, option g. 11/850 is the most accurate answer.