<u>Answer:</u>
96
<u>Step-by-step explanation:</u>
Let's assume that the marks needed in the next exam is . Then if the average becomes 90,
Now we can simply solve for :
⇒
⇒ [Multiplying both sides by 4]
⇒ [Subtracting 264 from both sides]
⇒
Therefore, you need to score 96 in your next exam to have an average of 90 on the four exams.
Given:
Two dice are rolled together.
Total number of possible outcomes.
To find:
The list of total possible outcomes.
The probability of getting a sum of 11 in these outcomes.
The probability of getting a sum less than or equal to 4.
The probability of getting a sum of 13 or more.
Solution:
If two dice are rolled together, then the total number of possible outcomes is 36 and list of total possible outcomes is
S = {(1,1),(1,2),(1,3),(1,4),(1,5),(1,6),(2,1),(2,2),(2,3),(2,4),(2,5),(2,6),(3,1),(3,2),(3,3),(3,4),(3,5),(3,6),(4,1),(4,2),(4,3),(4,4),(4,5),(4,6),(5,1),(5,2),(5,3),(5,4),(5,5),(5,6),(6,1),(6,2),(6,3),(6,4),(6,5),(6,6)}
Sum of 11 in these outcomes = {(5,6),(6,5),(6,6)} = 3
The probability of getting a sum of 11 in these outcomes is
Therefore, the probability of getting a sum of 11 in these outcomes is .
Sum less than or equal to 4 = {(1,1),(1,2),(1,3),(2,1),(2,2),(3,1)} = 6
The probability of getting a sum less than or equal to 4 is
Therefore, the probability of getting a sum less than or equal to 4 is .
Sum of 13 or more = empty set because maximum sum is 12.
The probability of getting a sum of 13 or more is
Therefore, the probability of getting a sum of 13 or more is 0.