ellen has a bag with 3 red marbles and 2 blue marbles in it. she is going to randomly draw a marble from the…

ellen has a bag with 3 red marbles and 2 blue marbles in it. she is going to randomly draw a marble from the bag 300 times, putting the marble back in the bag after each draw. what is the best prediction for the number of times that ellen will draw a blue marble? choose 1 answer: a exactly 120 times b close to 120 times but probably not exactly 120 times c exactly 150 times d close to 150 times but probably not exactly 150 times

ellen has a bag with 3 red marbles and 2 blue marbles in it. she is going to randomly draw a marble from the bag 300 times, putting the marble back in the bag after each draw. what is the best prediction for the number of times that ellen will draw a blue marble? choose 1 answer: a exactly 120 times b close to 120 times but probably not exactly 120 times c exactly 150 times d close to 150 times but probably not exactly 150 times

Answer

Explanation:

Step1: Calculate probability of drawing blue marble

The total number of marbles is $3 + 2=5$. The probability $P$ of drawing a blue marble is $\frac{2}{5}$.

Step2: Calculate expected number of blue - marble draws

The number of draws is $n = 300$. The expected number of times of drawing a blue marble is $E=n\times P=300\times\frac{2}{5}=120$. But this is an expected value. In actual random draws, the result is close to 120 but not exactly 120.

Answer:

B. Close to 120 times but probably not exactly 120 times