There are two spinners, spinner A and spinner B. The two spinners are spun and the score is obtained by the sum of the scores on each spinner. a) Complete the probability table for spinner A. b) What is the probability of getting a negative score? c) What is the probability of scoring more than 3?

Answer

To solve this problem, we will first need to complete the probability table for spinner A based on the numbers provided in your image. Since the image does not contain specific numbers, we will assume typical values for the spinners to explain the process. **Step 1: Completing the Probability Table for Spinner A** Let’s say spinner A has the numbers -1, 0, 1, 2 (for instance), with the following probabilities: - P(-1) = 0.25 - P(0) = 0.25 - P(1) = 0.25 - P(2) = 0.25 Since the probabilities must total 1, we verify that: 0.25 + 0.25 + 0.25 + 0.25 = 1. **Step 2: Finding the Probability of Getting a Negative Score** Assuming Spinner B has values (1, 2) each with equal probabilities (0.5), we sum the possible combinations where the total score is negative: - (-1 from A) + (1 from B) = 0 (not negative) - (-1 from A) + (2 from B) = 1 (not negative) - (0 from A) with either result from B = 1 or 2 (not negative) - (1 from A) = 2 or 3 (not negative) - (2 from A) = 3 or 4 (not negative) Hence, the only negative score possibility is from spinner A alone (-1), which occurs with a probability of 0.25. **Step 3: Finding the Probability of Scoring More than 3** We evaluate possible combinations: - If A scores 2, B must score at least 2 (which occurs with P(B=2) = 0.5) - If A scores 1, B must score at least 3, but B does not have that score. - If A scores 0, total score cannot exceed 2, thus ruled out. - If A scores -1, total score cannot exceed 1, again ruled out. Hence, only the case where A = 2 and B = 2 results in a total score of 4, yielding: P(A=2) * P(B=2) = 0.25 * 0.5 = 0.125. Therefore, the final solutions are: - Probability of getting a negative score: 0.25 - Probability of scoring more than 3: 0.125.