Question

2. Consider a ten-sided die of which the sides display the numbers 1, 2, 3, and 4 according to this table:
side of die 1 2 3 4 5 6 7 8 9 10 number displayed 1 1 1 1 2 2 2 3 3 4
Rolling two such dice is an experiment with the sample space S =       (1,1) (1,2) (1,3) (1,4) (2,1) (2,2) (2,3) (2,4) (3,1) (3,2) (3,3) (3,4) (4,1) (4,2) (4,3) (4,4)
      (a) Find the probability of the outcome (1,1). Hint: It is not one-sixteenth. (b) Find the probability of not rolling doubles. (c) Find the probability that the sum of the rolls is at least seven. (d) Find the probability that doubles are rolled given that the sum of the rolls is less than seven. (e) Find the probability that the sum of the rolls is less than seven given that doubles are rolled.

Answer 1

Total number of sides=10

Number of ones on the die=4

Number of twos on the die=3

Number of threes on the die=2

Number of fours on the die=1

a)The probability of the outcome (1,1)=

b) Probability of not rolling doubles=

c) Probability that the sum of the rows is at least 7=

d) Probability that doubles are rolled given that sum of rolls is less than 7=

e) Probability that the sum of the rolls is less than 7 given that doubles are rolled=