a bag has 2 blue marbles, 3 red marbles, and 5 white marbles. which events have a probability greater than…

a bag has 2 blue marbles, 3 red marbles, and 5 white marbles. which events have a probability greater than $\frac{1}{5}$? select three options.\nchoosing 1 blue marble\nchoosing 1 red marble\nchoosing 1 red marble, not replacing it, and then choosing a blue marble\nchoosing 1 white marble, replacing it, and choosing another white marble\nchoosing 1 white marble
Answer
Explanation:
Step1: Calculate total number of marbles
$2 + 3+5=10$
Step2: Calculate probability of choosing 1 blue marble
$P(\text{blue})=\frac{2}{10}=\frac{1}{5}$
Step3: Calculate probability of choosing 1 red marble
$P(\text{red})=\frac{3}{10}>\frac{1}{5}$
Step4: Calculate probability of choosing 1 red then 1 blue (without - replacement)
$P(\text{red then blue})=\frac{3}{10}\times\frac{2}{9}=\frac{6}{90}=\frac{1}{15}<\frac{1}{5}$
Step5: Calculate probability of choosing 1 white, replacing, then another white
$P(\text{white then white})=\frac{5}{10}\times\frac{5}{10}=\frac{25}{100}=\frac{1}{4}>\frac{1}{5}$
Step6: Calculate probability of choosing 1 white marble
$P(\text{white})=\frac{5}{10}=\frac{1}{2}>\frac{1}{5}$
Answer:
- choosing 1 red marble
- choosing 1 white marble, replacing it, and choosing another white marble
- choosing 1 white marble