Example 3: using the multiplication rule for independent events
a number cube has faces numbered 1 through 6, and a coin has two sides, heads and tails. the number cube will be rolled, and the coin will be flipped. find the probability that the cube
shows a 4 and the coin lands on heads. because the events are independent, we can use the multiplication rules we just learned.
if you toss the coin five times, what is the probability you will see a head on all five tosses?
if you tossed the coin five times and got five heads, would you think that this coin is a fair coin? why or why not?
if you roll the number cube three times, what is the probability that it will show 4 on all three throws?
if you rolled the number cube three times and got a 4 on all three rolls, would you think that this number cube is fair? why or why not?
suppose that the credit card company introduced in exercise 1 states that when a customer is selected at random, the probability that the customer pays his bill in full each month
is 0.35, the probability that the customer makes regular online purchases is 0.83, and these two events are independent. what is the probability that a randomly selected customer pays
his bill in full each month and makes regular online purchases?