A basketball player’s probability of making a free throw is 9/10. When the player shoots 2 free throws in a row, X is the number of free throws that score.
Create a probability distribution table for the variable X. Use the table to find the indicated probability.
Cannot draw tables on these posts.
If the events are independent, the probability of both/all events occurring is determined by multiplying the probabilities of the individual events.
p(0) = 1/10 * 1/10
P(1) = 9/10 * 1/10
P(2) = 9/10 * 9/10
To create a probability distribution table for the variable X, we need to consider all the possible outcomes when shooting 2 free throws.
The outcomes when shooting 2 free throws can be categorized into four possibilities:
- Both free throws scored (X = 2)
- Only the first free throw scored (X = 1)
- Only the second free throw scored (X = 1)
- Neither free throw scored (X = 0)
Now, let's calculate the probabilities for each outcome:
1. Both free throws scored (X = 2):
The probability of making a free throw is 9/10. Since there are two free throws, the probability of both free throws scoring is (9/10) * (9/10) = 81/100.
2. Only the first free throw scored (X = 1):
The probability of making the first free throw is 9/10, and the probability of missing the second free throw is 1 - (9/10) = 1/10. Thus, the probability of only the first free throw scoring is (9/10) * (1/10) = 9/100.
3. Only the second free throw scored (X = 1):
The probability of missing the first free throw is 1 - (9/10) = 1/10, and the probability of making the second free throw is 9/10. Therefore, the probability of only the second free throw scoring is (1/10) * (9/10) = 9/100.
4. Neither free throw scored (X = 0):
The probability of missing the first free throw is 1 - (9/10) = 1/10, and the probability of missing the second free throw is also 1 - (9/10) = 1/10. Consequently, the probability of neither free throw scoring is (1/10) * (1/10) = 1/100.
Now we can create the probability distribution table:
X | 0 | 1 | 2
--------------------------
P(X) | 1/100 | 18/100 | 81/100
To find a specific probability, you can refer to the table. For example, the probability of scoring exactly one free throw (X = 1) is 18/100.