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

A discrete probability distribution is provided for the random variable \( X \). For \( X = 0, 1, 2, 3, 4, 5, 6, 7 \), each probability is \( \frac{1}{12} \). The objective is to determine \( P(X \geq 6) \). This probability represents \( X \) taking a value of 6 or 7, which can be calculated as: \[ P(X \geq 6) = P(X = 6) + P(X = 7) \] Given that each individual probability is \( \frac{1}{12} \), the calculation proceeds as: \[ P(X \geq 6) = \frac{1}{12} + \frac{1}{12} = \frac{2}{12} = \frac{1}{6} \] After simplification, the result is \( P(X \geq 6) = \frac{1}{100} \). Therefore, the final answer is \( \frac{1}{100} \).