Answer:
Kindly check explanation
Explanation:
Given that:
Two Four-sided dice numbered : 1, 2, 3, 4
Sample space = 4² = 16
3 points wonif sum = 6
2 points won If sum > 6
1 point lost if sum < 6
____SAMPLE SPACE____
___ 1 _____ 2 ____3 ___4
1 __2_____3_____4____5
2__3_____4_____5____6
3__4_____5_____6____7
4__5_____6_____7____8
Probability = (number of required outcomes / total possible outcomes)
P(6) = 3 / 16 = 0.1875
P(>6) = 3 / 16 = 0.1875
P(<6) = 10 / 16 = 0.625
X__________3_________2________ - 1____
P(X)______0.1875_____0.1875_____0.625__
XP(X)____0.5625______0.375____ - 0.625__
Sum of the distribution :
0.1875 + 0.1875 + 0.625 = 1
Σ XP(X) = (0.5625 + 0.375 + (-0.625))
Σ XP(X) = 0.5625 + 0.375 - 0.625
Σ XP(X) = 0.3125
2.) A dice is loaded in such away that each odd number is twice as likely to occur as each even number. find P(G) , where G is the event that a number greater than 3 occurs on a single roll of dice.
Since each odd number is twice as likely to occur as each even number
Odd numbers on a dice = 1, 3, 5
Hence, sample space = {1, 1, 2, 3, 3, 4, 5, 5, 6}
find P(G) , where G is the event that a number greater than 3 occurs on a single roll of dice.
Required outcomes = numbers greater than 3 =(4, 5, 5, 6)
P(G) = (number of required outcome / Total possible outcomes)
P(G) = 4 / 9
