Question

Craig and Danny are planning to tr y out for the basketball team and one of the criteria fro the selection is based on free throw shots. Craig makes 55% of the free throwshe attempts, while Danny makes 71% of the free throws he attempts. Which is more likely: that Craig will miss two free shot throws in a row, or that Danny will make three free throw shots in a row?

Answer 1

It is more likely that Danny will make three free throw shots in a row.

Explanation:

The probabilities of Craig and Danny making the throw they attempt, is given as:

Probability that Craig will make the throw = 55% = 0.55

Probability that Danny will make the throw = 71% = 0.71

Now, the probabilities that they will miss the throw can be found out by subtracting the probabilities, that they can make the throw, from 1.

Probability that Craig will miss the throw = 1 - 0.55 = 0.45

Probability that Danny will miss the throw = 1 - 0.71 = 029

Now,

Probability that Craig will miss two throws in a row = (0.45)(0.45) Probability that Craig will miss two throws in a row = 0.2025

And,

Probability that Danny will make three throws in a row = (0.71)(0.71)(0.71)

Probability that Danny will make three throws in a row = 0.3579

Since, the probability of Danny making three throws in a row is higher than the probability of Craig missing two throws in a row.

Thus, it is clear that, it is more likely that Danny will make three free throw shots in a row.