What's left in the bag:
4R, 4G, 3B, 4W = 15 marbles total
Expected value
= ∑ x P(x)
=(4*1+4*2+3*3+4*10)/15
=4.07
Part A: If Noor draws a marble next, what is the expected value of Noor’s marble? Show your work.
Part B: Does this mean that Noor is more likely to win than to lose? Explain your answer.
4R, 4G, 3B, 4W = 15 marbles total
Expected value
= ∑ x P(x)
=(4*1+4*2+3*3+4*10)/15
=4.07
Before Jeremy drew a blue marble, there were a total of 4 red marbles, 4 green marbles, 3 blue marbles, and 4 white marbles in the bag.
Now, let's calculate the probabilities of each possible outcome for Noor's draw:
1. Drawing a red marble: There are 4 red marbles remaining out of 15 total marbles.
Probability = 4/15
Point value = 1
2. Drawing a green marble: There are still 4 green marbles remaining out of 15 total marbles.
Probability = 4/15
Point value = 2
3. Drawing a blue marble: There are 2 blue marbles left out of 15 total marbles (Jeremy took 1 blue marble).
Probability = 2/15
Point value = 3
4. Drawing a white marble: There are still 4 white marbles remaining out of 15 total marbles.
Probability = 4/15
Point value = 10
Now, we can calculate the expected value using the formula:
Expected value = (Probability of outcome 1 × Point value of outcome 1) + (Probability of outcome 2 × Point value of outcome 2) + (Probability of outcome 3 × Point value of outcome 3) + (Probability of outcome 4 × Point value of outcome 4)
Expected value = (4/15 × 1) + (4/15 × 2) + (2/15 × 3) + (4/15 × 10)
Expected value = 4/15 + 8/15 + 6/15 + 40/15
Expected value = 58/15
Expected value ≈ 3.87 points
Therefore, the expected value of Noor's marble is approximately 3.87 points.
Part B: The expected value tells us the average number of points Noor can expect to get when she draws a marble. In this case, Noor's expected value is 3.87 points. Since the maximum possible points for a single marble is 10, it means Noor is more likely to win than to lose. However, it does not guarantee her victory in any one draw. It simply suggests that if the game were to be played many times, Noor would likely accumulate more points than Jeremy over time.