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quokkamokka97
28.07.2020 •
Mathematics
There are 4 red balls and 6 green balls in a bag.
You reach in the bag and take out 3 balls without looking.
What is the probability that all three of the balls you take out are red?
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Ответ:
![\frac{1}{30}](/tpl/images/0714/2353/d0f93.png)
Step-by-step explanation:From the question, in the bag there are;
4 red balls
6 green balls
10 balls in total.
Now, reaching in the bag and taking out 3 balls without looking, the probability that all three balls are red, can be analyzed as follows;
All three red means;
The first ball is red,
The second ball is red and;
The third ball is red.
i. First you take out a ball from a total of 10 balls. The probability P⁰(R) of having a red ball is given as;
P⁰(R) =![\frac{possible-space}{total-space}](/tpl/images/0714/2353/c2f7d.png)
Since there are 4 red balls, the possible-space is 4
Also, since there are a total of 10 balls, the total-space is 10
P⁰(R) =![\frac{4}{10} = \frac{2}{5}](/tpl/images/0714/2353/553a4.png)
ii. Secondly, you take out a ball from a remaining total of 9 balls. The probability P¹(R) of still having a red ball is given as;
P¹(R) =![\frac{possible-space}{total-space}](/tpl/images/0714/2353/c2f7d.png)
Since there are 3 red balls remaining, the possible-space is 3
Also, since there are a remaining total of 9 balls, the total-space is 9
P¹(R) =![\frac{3}{9} = \frac{1}{3}](/tpl/images/0714/2353/a75a1.png)
iii. Thirdly, you take out a ball from a remaining total of 8 balls. The probability P²(R) of still having a red ball is given as;
P²(R) =![\frac{possible-space}{total-space}](/tpl/images/0714/2353/c2f7d.png)
Since there are 2 red balls remaining, the possible-space is 2
Also, since there are a remaining total of 8 balls, the total-space is 8
P²(R) =![\frac{2}{8} = \frac{1}{4}](/tpl/images/0714/2353/74932.png)
Therefore, the probability P(R) of taking out three red balls without looking is given by the product of the probabilities described above. i.e
P(R) = P⁰(R) x P¹(R) x P²(R)
P(R) =![\frac{2}{5} * \frac{1}{3} * \frac{1}{4} = \frac{1}{30}](/tpl/images/0714/2353/c41bb.png)
Ответ:
$28080 per year
Step-by-step explanation:
15$ per hour for the first job and she does it for 10 hours each week, this means, 15*10 which is 150. So we have 150 for the 1st job every week.
2nd job, 13$ per hour. She does that for 30 hours a week so we have 13*30 which is 390$ per week.
The two jobs together are 150 per week and 390 per week which means 540$ per week. Now` if we want to find how much she makes in a year, the are 52 weeks in a year, so multiply 540$ *52=$28080
So she makes $28080 per year