Question
Following is the probability distribution of a random variable that represents the number of extracurricular activities a college freshman participates in.
x|0 1 2 3 4
P(x)| 0.04 0.14 0.47 0.22 0.13
(a) Find the probability that a student participates in exactly three activities.
The probability that a student participates in exactly three activities is
x|0 1 2 3 4
P(x)| 0.04 0.14 0.47 0.22 0.13
(a) Find the probability that a student participates in exactly three activities.
The probability that a student participates in exactly three activities is
Answers
Answer
b) Find the probability that a student participates in more than two activities.
Answer
(c) Find the probability that a student participates in at least one activity.
Answered by
GPT-4o mini
To find the probability that a student participates in exactly three activities, we can look at the provided probability distribution.
From the table given:
- For \( x = 3 \), \( P(x) = 0.22 \).
Thus, the probability that a student participates in exactly three activities is:
\[
\text{The probability that a student participates in exactly three activities is } 0.22.
\]
From the table given:
- For \( x = 3 \), \( P(x) = 0.22 \).
Thus, the probability that a student participates in exactly three activities is:
\[
\text{The probability that a student participates in exactly three activities is } 0.22.
\]
Answered by
GPT-4o mini
To find the probability that a student participates in more than two activities, we need to consider the probabilities for \( x = 3 \) and \( x = 4 \).
From the given probability distribution:
- \( P(3) = 0.22 \) (for 3 activities)
- \( P(4) = 0.13 \) (for 4 activities)
Now, we can sum these probabilities:
\[
P(x > 2) = P(3) + P(4) = 0.22 + 0.13 = 0.35
\]
Therefore, the probability that a student participates in more than two activities is:
\[
\text{The probability that a student participates in more than two activities is } 0.35.
\]
From the given probability distribution:
- \( P(3) = 0.22 \) (for 3 activities)
- \( P(4) = 0.13 \) (for 4 activities)
Now, we can sum these probabilities:
\[
P(x > 2) = P(3) + P(4) = 0.22 + 0.13 = 0.35
\]
Therefore, the probability that a student participates in more than two activities is:
\[
\text{The probability that a student participates in more than two activities is } 0.35.
\]
Answered by
GPT-4o mini
To find the probability that a student participates in at least one activity, we need to consider the probabilities for \( x = 1, 2, 3, \) and \( 4 \). Alternatively, since we know the total probability must sum to 1, we can also find this probability by subtracting the probability of not participating in any activities (i.e., \( x = 0 \)) from 1.
From the given probability distribution:
- \( P(0) = 0.04 \) (for 0 activities)
Now, we can calculate the probability of participating in at least one activity:
\[
P(x \geq 1) = 1 - P(0) = 1 - 0.04 = 0.96
\]
Therefore, the probability that a student participates in at least one activity is:
\[
\text{The probability that a student participates in at least one activity is } 0.96.
\]
From the given probability distribution:
- \( P(0) = 0.04 \) (for 0 activities)
Now, we can calculate the probability of participating in at least one activity:
\[
P(x \geq 1) = 1 - P(0) = 1 - 0.04 = 0.96
\]
Therefore, the probability that a student participates in at least one activity is:
\[
\text{The probability that a student participates in at least one activity is } 0.96.
\]