Question

Shandelle rolls a pair of fair dice and sums the number of spots that appear on the up faces. She then flips a fair coin the number times associated with the sum of the spots. For example, if she rolled a 3 and a 4, then she flips the fair coin 7 times. If the coin flipping part of the random experiment yielded an equal number of heads and tails, find the probability that she rolled an 8 on the dice rolling part of the random experiment. Write a Monte Carlo simulation in R to support the analytic solution.

Answer 1

Sample(Event) space of getting equal number of heads and tails : (1,1),(2,2),(3,3),(4,4) (5,5),(6,6) i.e on the dice rolling part of the experiment she would have got 2 (1+1),4(2+2),6(3+3),8(4+4),10(5+5),12(6+6)

Therefore

Number of ways of getting equal number of heads and tails = 6

Event of  getting a 8 on the dice rolling part of the experiment is (4,4) : Given that coin flipping part of the random experiment yielded an equal number of heads and tails

Number of ways of getting a 8 on the dice rolling part of the experiment : Given that coin flipping part of the random experiment yielded an equal number of heads and tails, i.e From the event space = 1

probability that she rolled an 8 on the dice rolling part of the random experiment, If the coin flipping part of the random experiment yielded an equal number of heads and tails

= Number of ways of getting a 8 on the dice rolling part of the experiment : Given that coin flipping part of the random experiment yielded an equal number of heads and tails, i.e From the event space / Number of ways of getting equal number of heads and tails

= 1/6=0.1667

If the coin flipping part of the random experiment yielded an equal number of heads and tails, the probability that she rolled an 8 on the dice rolling part of the random experiment = 1/6 = 0.1667