a) the number that should replace A is 6 and b) The probability of the total being 4 is 1/16.
a) To find the number that should replace A, we need to analyze the diagram. The diagram shows the totals obtained by adding together the results from spinning two fair four-sided spinners. Looking at the diagram, we can see that the total for the combination of 1 and 2 is 3, the total for the combination of 1 and 3 is 5, and the total for the combination of 2 and 3 is 6.
To find the missing number, we need to determine the missing total. Since each spinner has four sides, we know that the possible outcomes for each spinner are 1, 2, 3, and 4. To find the missing total, we can use the information we have about the other totals.
From the diagram, we can see that the total for the combination of 1 and 4 is 6, and the total for the combination of 3 and 4 is 7. Since these are the only two possible combinations involving 4, the missing total must be 6.
b) To find the probability of the total being 4, we need to determine the number of favorable outcomes and the total number of possible outcomes. In this case, the favorable outcomes are the combinations that result in a total of 4.
Looking at the diagram, we can see that the only combination that results in a total of 4 is the combination of 1 and 3. Therefore, there is only 1 favorable outcome.
Now, let's determine the total number of possible outcomes. Since each spinner has four sides, there are a total of 4 possible outcomes for each spinner. To find the total number of possible outcomes when spinning both spinners, we multiply the number of outcomes for each spinner. So, there are 4 * 4 = 16 possible outcomes.