you spin the spinner, pick a card, roll a die, and find the sum. how many different sums are possible?

Answer

Explanation:

Step1: Determine the number of outcomes for each event

Spinner has 2 outcomes (1, 2), cards have 2 outcomes (4, 5), die has 6 outcomes (1 - 6).

Step2: Find the minimum sum

The minimum sum occurs when we get 1 from spinner, 4 from cards and 1 from die. So minimum sum is (1 + 4+1=6).

Step3: Find the maximum sum

The maximum sum occurs when we get 2 from spinner, 5 from cards and 6 from die. So maximum sum is (2 + 5+6 = 13).

Step4: Analyze possible sums

The possible sums range from 6 to 13. The number of integers in the range from (a) to (b) (inclusive) is (b - a+1). Here (a = 6) and (b = 13), so the number of different sums is (13 - 6 + 1=8).