If there are 700 students in a school and 450 of them carry a mobile device, what is the

Question

probability that when 4 students are randomly selected, that at least 3 of them carry a mobile
device?

Answer 1

To find the probability of at least 3 students carrying a mobile device when 4 are selected randomly, we can determine the probabilities of exactly 3 of them carrying one and all 4 carrying one, and then add those probabilities together.

Let S (students carrying mobile device) = 450 and T (total students) = 700

1. Probability that exactly 3 students have a mobile device and 1 student does not:

- Ways to pick 3 students with a mobile device (combinatorial formula: nCr): 450C3
- Ways to pick 1 student without a mobile device (combinatorial formula, removing the 450 mobile students from the total count): 250C1
- Ways to pick any 4 students from the total: 700C4

So, the probability for this case: (450C3 * 250C1) / 700C4

2. Probability that all 4 students have a mobile device:

- Ways to pick 4 students with a mobile device: 450C4
- Ways to pick any 4 students from the total: 700C4

So, the probability for this case: 450C4 / 700C4

Now, add the probabilities for both cases:

(450C3 * 250C1) / 700C4 + 450C4 / 700C4

Using the combinatorial formula, we get:

(450! / (3! * 447!)) * (250! / (1! * 249!)) / (700! / (4! * 696!)) + (450! / (4! * 446!)) / (700! / (4! * 696!))

Simplifying the expression, we get:

(11,198,100 * 250 + 67,425) / 84,270,245

Computing the numerical values, we get:

(2,799,525,000 + 67,425) / 84,270,245

2,799,592,425 / 84,270,245 = approximately 0.332308

So the probability that at least 3 out of 4 randomly selected students carry a mobile device is approximately 0.332308 or 33.23%.