sophia has a bag with 3 purple marbles and 4 blue marbles in it. she is going to randomly draw a marble from…

sophia has a bag with 3 purple marbles and 4 blue marbles in it. she is going to randomly draw a marble from the bag 280 times, putting the marble back in the bag after each draw. complete the following statement with the best prediction. sophia will draw a purple marble... choose 1 answer: a exactly 120 times b close to 120 times but probably not exactly 120 times c exactly 160 times d close to 160 times but probably not exactly 160 times

sophia has a bag with 3 purple marbles and 4 blue marbles in it. she is going to randomly draw a marble from the bag 280 times, putting the marble back in the bag after each draw. complete the following statement with the best prediction. sophia will draw a purple marble... choose 1 answer: a exactly 120 times b close to 120 times but probably not exactly 120 times c exactly 160 times d close to 160 times but probably not exactly 160 times

Answer

Explanation:

Step1: Calculate probability of drawing purple marble

The total number of marbles is $3 + 4=7$. The probability of drawing a purple marble $P(\text{purple})=\frac{3}{7}$.

Step2: Calculate expected number of purple - marble draws

The number of draws is $n = 280$. The expected number of times to draw a purple marble is $E=n\times P(\text{purple})=280\times\frac{3}{7}=120$. Since this is a probability - based experiment, we expect to get close to 120 times but not exactly 120 times.

Answer:

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