Answer:
20
Step-by-step explanation:
6x^2-5x+3 - (3x^2+8x-4)
2 answers:
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Answer:
There are 12 sets of four marbles include all the red ones.
Step-by-step explanation:
Given : A bag contains three red marbles, two green ones, one lavender one, four yellows, and five orange marbles.
To find : How many sets of four marbles include all the red ones?
Solution :
Number of red marbles = 3
Number of green marbles = 2
Number of lavender marbles = 1
Number of yellow marbles = 4
Number of orange marbles = 5
We have to form sets of four marbles include all the red ones,
For position of getting red ones we have three red marbles i.e.
For the fourth one we have 12 choices i.e.
Total sets of four marbles include all the red ones is
Therefore, There are 12 sets of four marbles include all the red ones.
Answer:
The probability is 0.0052
Step-by-step explanation:
Let's call A the event that the four cards are aces, B the event that at least three are aces. So, the probability P(A/B) that all four are aces given that at least three are aces is calculated as:
P(A/B) = P(A∩B)/P(B)
The probability P(B) that at least three are aces is the sum of the following probabilities:
- The four card are aces: This is one hand from the 270,725 differents sets of four cards, so the probability is 1/270,725
- There are exactly 3 aces: we need to calculated how many hands have exactly 3 aces, so we are going to calculate de number of combinations or ways in which we can select k elements from a group of n elements. This can be calculated as:
So, the number of ways to select exactly 3 aces is:
Because we are going to select 3 aces from the 4 in the poker deck and we are going to select 1 card from the 48 that aren't aces. So the probability in this case is 192/270,725
Then, the probability P(B) that at least three are aces is:
On the other hand the probability P(A∩B) that the four cards are aces and at least three are aces is equal to the probability that the four card are aces, so:
P(A∩B) = 1/270,725
Finally, the probability P(A/B) that all four are aces given that at least three are aces is: