What is the combined probability of the following events occurring: rolling 1 or
6 on a fair die, flipping 2 heads in a row on a fair coin, then rolling 2,3,4 or
5 on the same die.
That's four events in succession:
A. 2 ways out of 6 that the die can fall successfully, a probability of 2/6 which
reduces to 1/3.
B. 1 way out of 2 ways the fair coin can fall successfully the first time, a
probability of 1/2.
C. 1 way out of 2 ways the fair coin can fall successfully the second time, also
a probability of 1/2.
D. 4 ways out of 6 that the die can fall successfully, a probability of 4/6 which
reduces to 2/3.
For those 4 events to occur in succession, the probability is the product of the
probabilities, since they are independent events.
Answer: (1/3)(1/2)(1/2)(2/3) = 2/36 which reduces to 1/18.
Edwin