In a high school basketball game, a player on the home team makes two free throws. One student asks the student next to her what he thinks the probability of hitting two free throws in a row is. The student replies, "The probability of him making a free throw is probably about .6, so hitting two free throws is probably about 1.2." Why can this immediately be dismissed as incorrect?
A. The final number, 1.2, is a fraction, which can never represent a probability.
B. The probability of making a free throw can never be .6.
C. The probability of an event happening twice in a row can never be equal.
D. The final number is greater than 1, which is not a valid probability.
D, If the events are independent, the probability of both/all events occurring is determined by multiplying the probabilities of the individual events.
The correct answer is D. The final number is greater than 1, which is not a valid probability.
To understand why this statement is incorrect, let's break it down step by step. The student claimed that the probability of making a free throw is probably about 0.6. This means that in a given free throw attempt, there is an estimated 60% chance of the player successfully making the shot.
However, when calculating the probability of two independent events occurring in succession, you multiply the probabilities together. In this case, the student mistakenly added the probabilities instead of multiplying them. By adding 0.6 and 0.6, the student arrived at the incorrect result of 1.2.
In probability theory, a probability can never be greater than 1. A probability of 1 represents a 100% chance of an event occurring, while a probability of 0 represents a 0% chance. Any value between 0 and 1 represents the likelihood of an event happening on a scale from impossible to certain.
Therefore, since the final number of 1.2 is greater than 1, it cannot represent a valid probability and can be dismissed as incorrect.