In: Statistics and Probability
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