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Ellen has a bag with red marbles and blue marbles in it. She is going to randomly draw a marble from the bag 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 answer:(A) Exactly times(B) Close to times but probably not exactly times(C) Exactly times(D) Close to times but probably not exactly times
Full solution
Q. Ellen has a bag with red marbles and blue marbles in it. She is going to randomly draw a marble from the bag 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 answer:(A) Exactly times(B) Close to times but probably not exactly times(C) Exactly times(D) Close to times but probably not exactly times
- Determine Probability of Blue Marble: First, we need to determine the probability of drawing a blue marble in a single draw. Since there are red marbles and blue marbles, the total number of marbles is . The probability of drawing a blue marble is the number of blue marbles divided by the total number of marbles.
- Calculate Probability of Drawing Blue Marble: Now, let's calculate the probability of drawing a blue marble. Probability of drawing a blue marble Number of blue marbles Total number of marbles .
- Predict Number of Blue Marble Draws: Next, we will use this probability to predict the number of times a blue marble will be drawn out of draws.Since each draw is independent and the marble is replaced each time, we can multiply the probability of drawing a blue marble by the total number of draws to get the expected number of times a blue marble will be drawn.
- Perform Calculation for Expected Draws: Let's perform the calculation for the expected number of blue marble draws. Expected number of blue marble draws = Probability of drawing a blue marble Total number of draws = .
- Compute Expected Number of Blue Marble Draws: Now, we will compute the expected number of blue marble draws. Expected number of blue marble draws = .
- Interpret Result: Finally, we need to interpret the result. The calculation gives us the expected value, which is the best prediction for the average outcome over many trials. However, in any given set of draws, the actual number of times a blue marble is drawn is likely to be close to but not exactly times due to the randomness of each draw.
