MATH SOLVE

4 months ago

Q:
# An experiment consists of drawing a marble out of a bag, observing the color, and then placing it back in the bag. Suppose the experiment is repeated 75 times, with the following results: red 38 blue 23 green 11 yellow 3 What is the probability of drawing two yellow marbles in a row

Accepted Solution

A:

The experimental data suggest that

[tex]\mathbb P(\text{red})\approx\dfrac{38}{75}[/tex]

[tex]\mathbb P(\text{blue})\approx\dfrac{23}{75}[/tex]

[tex]\mathbb P(\text{green})\approx\dfrac{11}{75}[/tex]

[tex]\mathbb P(\text{yellow})\approx\dfrac3{75}[/tex]

Because the marble is replaced after being drawn, and so the number of marbles of a given color remains the same, the event of drawing any given color is independent of what was drawn before. So

[tex]\mathbb P(\text{2 consecutive yellows})\approx\dfrac3{75}\cdot\dfrac3{75}=\dfrac1{625}[/tex]

[tex]\mathbb P(\text{red})\approx\dfrac{38}{75}[/tex]

[tex]\mathbb P(\text{blue})\approx\dfrac{23}{75}[/tex]

[tex]\mathbb P(\text{green})\approx\dfrac{11}{75}[/tex]

[tex]\mathbb P(\text{yellow})\approx\dfrac3{75}[/tex]

Because the marble is replaced after being drawn, and so the number of marbles of a given color remains the same, the event of drawing any given color is independent of what was drawn before. So

[tex]\mathbb P(\text{2 consecutive yellows})\approx\dfrac3{75}\cdot\dfrac3{75}=\dfrac1{625}[/tex]