Respuesta :
Answer:
choosing 1 red marble ; choosing 1 white marble, replacing it, and choosing another white marble ; and choosing 1 white marble
Step-by-step explanation:
There are 2+3+5 = 10 marbles. The probability of choosing 1 blue marble is 2/10 = 1/5; this is not greater than 1/5.
The probability of choosing 1 red marble is 3/10; this is greater than 2/10, which is the same as 1/5.
The probability of choosing 1 red marble is 3/10; not replacing it and choosing a blue marble would then be a probability of 2/9. Together this is a probability of 3/10(2/9) = 6/90 = 3/45; this is smaller than 9/45, which is the same as 1/5.
The probability of choosing 1 white marble is 5/10 = 1/2; replacing it and choosing another white marble would be 1/2. Together this is a probability of 1/2(1/2) = 1/4; this is greater than 4/20, which is the same as 1/5.
The probability of choosing 1 white marble is 5/10 = 1/2. This is greater than 2/10, which is the same as 1/5.
The events that have a probability greater than [tex]\frac{1}{5}[/tex] are:
- Choosing a red marble
- Choosing a white marble, replacing it, and choosing another white marble is
- Choosing a white marble
We have a total of [tex]2\text{ blue }+3\text{ red }+5\text{ white marbles}[/tex], or [tex]10\text{ marbles}[/tex].
The probability of choosing [tex]1[/tex] blue marble is
[tex]\dfrac{2}{10}=\dfrac{1}{5}[/tex]
The probability of choosing a red marble is
[tex]\dfrac{3}{10}>\dfrac{1}{5}[/tex]
The probability of choosing a red marble, not replacing it, and then choosing a blue marble is
[tex]\dfrac{3}{10}\times \dfrac{2}{9}=\dfrac{1}{15}<\dfrac{1}{5}[/tex]
The probability of choosing a white marble, replacing it, and choosing another white marble is
[tex]\dfrac{5}{10}\times\dfrac{5}{10}=\dfrac{1}{4}>\dfrac{1}{5}[/tex]
The probability of choosing a white marble
[tex]\dfrac{5}{10}=\dfrac{1}{2}>\dfrac{1}{5}[/tex]
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