Answer:
true
Step-by-step explanation:
Using it's concept, it is found that there is a 0.0366 = 3.66% probability that your coach and your friend get orange and you get a fruit-punch.
<h3>What is a probability?</h3>
A probability is given by the <u>number of desired outcomes divided by the number of total outcomes</u>.
In this problem, there are 15 bottles.
- 5 are orange, hence the is a 5/15 = 1/3 probability that the coach gets orange, hence P(A) = 1/3.
- After the coach, there will be 14 bottles remaining, of which 4 are orange, hence the probability that the friend gets orange is of P(B) = 4/14 = 2/7.
- For you, there will be 13 bottles remaining, of which 5 will be of fruit-punch, hence the probability you get fruit-punch is of P(C) = 5/13.
The probability of the three outcomes occurring is given by:
![p = \frac{1}{3} \times \frac{2}{7} \frac{5}{13} = \frac{10}{273} = 0.0366](https://tex.z-dn.net/?f=p%20%3D%20%5Cfrac%7B1%7D%7B3%7D%20%5Ctimes%20%5Cfrac%7B2%7D%7B7%7D%20%5Cfrac%7B5%7D%7B13%7D%20%3D%20%5Cfrac%7B10%7D%7B273%7D%20%3D%200.0366)
0.0366 = 3.66% probability that your coach and your friend get orange and you get a fruit-punch.
More can be learned about probabilities at brainly.com/question/14398287
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The answer is 3. I don't know if you want ne to explain or show my work just reply to me.
Answer:
![P(A \cap B)](https://tex.z-dn.net/?f=%20P%28A%20%5Ccap%20B%29)
And we can use the following formula:
![P(A \cap B)= P(A)* P(B)](https://tex.z-dn.net/?f=%20P%28A%20%5Ccap%20B%29%3D%20P%28A%29%2A%20P%28B%29)
And replacing the info we got:
![P(A \cap B) = \frac{5}{7} \frac{2}{3}= \frac{10}{21}=0.476](https://tex.z-dn.net/?f=%20P%28A%20%5Ccap%20B%29%20%3D%20%5Cfrac%7B5%7D%7B7%7D%20%5Cfrac%7B2%7D%7B3%7D%3D%20%5Cfrac%7B10%7D%7B21%7D%3D0.476)
Step-by-step explanation:
We define two events for this case A and B. And we know the probability for each individual event given by the problem:
![p(A) = \frac{5}{7}](https://tex.z-dn.net/?f=%20p%28A%29%20%3D%20%5Cfrac%7B5%7D%7B7%7D)
![p(B) = \frac{2}{3}](https://tex.z-dn.net/?f=%20p%28B%29%20%3D%20%5Cfrac%7B2%7D%7B3%7D)
And we want to find the probability that A and B both occurs if A and B are independent events, who menas the following conditions:
![P(A|B) = P(A)](https://tex.z-dn.net/?f=%20P%28A%7CB%29%20%3D%20P%28A%29)
![P(B|A) = P(B)](https://tex.z-dn.net/?f=%20P%28B%7CA%29%20%3D%20P%28B%29)
And for this special case we want to find this probability:
![P(A \cap B)](https://tex.z-dn.net/?f=%20P%28A%20%5Ccap%20B%29)
And we can use the following formula:
![P(A \cap B)= P(A)* P(B)](https://tex.z-dn.net/?f=%20P%28A%20%5Ccap%20B%29%3D%20P%28A%29%2A%20P%28B%29)
And replacing the info we got:
![P(A \cap B) = \frac{5}{7} \frac{2}{3}= \frac{10}{21}=0.476](https://tex.z-dn.net/?f=%20P%28A%20%5Ccap%20B%29%20%3D%20%5Cfrac%7B5%7D%7B7%7D%20%5Cfrac%7B2%7D%7B3%7D%3D%20%5Cfrac%7B10%7D%7B21%7D%3D0.476)