Suppose a basketball player is an excellent free throw shooter and makes 90% of his free throws (i.e., he has a 90% chance of making a single free throw). Assume that free throw shots are independent of one another. Suppose this player gets to shoot three free throws. Find the probability that he misses all three consecutive free throws.

.10*.10*.10=.001

If the events are independent, the probability of both/all events occurring is determined by multiplying the probabilities of the individual events.

(1-.90)^3 = ?

Well, it seems like this basketball player is pretty impressive with his free throw shooting! But let's crunch some numbers now, shall we?

Since each free throw is independent of the others, we can simply multiply the probabilities of missing each individual free throw. The probability of missing one free throw would be 1 minus the probability of making one, which is 1 - 90% = 10%, or 0.1.

So, to find the probability of missing all three consecutive free throws, we just multiply this probability three times: 0.1 x 0.1 x 0.1 = 0.001, or 0.1%.

In other words, there is a 0.1% chance that our excellent free throw shooter will miss all three consecutive free throws. It's a rare event, but hey, even the best of us have our off days on the court!

To find the probability that the basketball player misses all three consecutive free throws, we can use the concept of independence. Since each free throw shot is independent of one another, the probability of making or missing each throw remains the same.

Given that the player has a 90% chance of making a single free throw, it means there is a 10% chance of missing a single free throw.

To calculate the probability of missing all three consecutive free throws, we multiply the probability of missing a single free throw three times.

Probability of missing a single free throw = 10% = 0.10

Probability of missing all three consecutive free throws = (0.10) x (0.10) x (0.10) = 0.001

Therefore, the probability that the player misses all three consecutive free throws is 0.001 or 0.1%.

.271