Question

Nina has 6 music sessions in a week. She attends the sessions 6 days a week 40% of the time, 5 days 18% of the time, one day 7% of the time, and no days 35% of the time. Let, X be a discrete random variable representing the number of sessions she attends in a week. Suppose one week is randomly selected, what is the probability that the random variable X take the value at most 5?

Answer 1

The probability that the random variable X takes the value at most 5 is 100%.

Step-by-step explanation:

To find the probability that the random variable X takes the value at most 5, we need to calculate the probability that Nina attends 0, 1, 2, 3, 4, or 5 music sessions in a week.

The probability that she attends 0 sessions is 35%. The probability that she attends 1 session is 7%. The probability that she attends 2 sessions is 18%. The probability that she attends 3 sessions is 40%. The probability that she attends 4 sessions is 0% (since the given percentages do not account for 4 sessions). And the probability that she attends 5 sessions is also 0%.

To find the probability of X being at most 5, we add up these probabilities: 35% + 7% + 18% + 40% + 0% + 0% = 100%.

Therefore, the probability that X takes the value at most 5 is 100%.

Answer 2

To calculate the probability that the random variable X takes a value at most 5, sum up the probabilities of attending the music sessions for each scenario and divide by the total number of sessions.

Step-by-step explanation:

The random variable X represents the number of music sessions Nina attends in a week. To find the probability that X takes a value at most 5, we need to find the sum of the probabilities of the random variable taking the values from 0 to 5. Here's how to calculate it:

• First, calculate the probability of attending the sessions 6 days a week: 6 days * 40% = 2.4 days
• Next, calculate the probability of attending the sessions 5 days a week: 5 days * 18% = 0.9 days
• Then, calculate the probability of attending the sessions one day a week: 1 day * 7% = 0.07 days
• Finally, sum up all the probabilities: 2.4 + 0.9 + 0.07 = 3.37 days

Therefore, the probability that the random variable X takes a value at most 5 is 3.37 out of 6. So the probability is 3.37/6 = 0.562 (approximately).