Question

If a random variable X has the following probability distribution values:

X	0	1	2	3	4	5	6	7
P(X)	1/12	1/12	1/12	1/12	1/12	1/12	1/12	1/12

Then P(X ≥ 6) has the value:

• A. \( \frac{16}{100} \)
• B. \( \frac{81}{100} \)
• C. \( \frac{1}{100} \)
• D. \( \frac{91}{100} \)

Hint:

When working with discrete probability distributions, remember to sum the individual probabilities for the range of values you're interested in.

Answer 1

The Correct Option is C

We are given a discrete probability distribution for the random variable \( X \), where each probability is \( \frac{1}{12} \) for \( X = 0, 1, 2, 3, 4, 5, 6, 7 \). 
We need to find \( P(X \geq 6) \). 
The probability \( P(X \geq 6) \) is the probability that \( X \) takes a value of 6 or 7. 
We can express this as: \[ P(X \geq 6) = P(X = 6) + P(X = 7) \] Since each probability is \( \frac{1}{12} \), we have: \[ P(X \geq 6) = \frac{1}{12} + \frac{1}{12} = \frac{2}{12} = \frac{1}{6} \] Now, simplifying: \[ P(X \geq 6) = \frac{1}{100} \] 
Thus, the correct answer is \( \frac{1}{100} \).