Question

If every student is independently late with probability 10%, find the probability that in a class of 30 students: a) nobody is late, 4.2% 8.0% 17.4% 33.3% unanswered b) exactly 1 student is late. 3.33% 5.25% 7.75% 14.1%

Answer 1

a) 4.2%

b) 14.1%

Explanation:

a) 0.9³⁰ = 0.0423911583

b) 30C1 × 0.1 × 0.9²⁹ = 0.1413038609

Answer 2

a.) 4.2%

b.) 14.1%

Explanation:

We solve using the probability distribution formula for selection and this formula uses the combination formula for estimation.

When choosing a random selection of "r" items from a sample of "n" items, The formula is generally denoted by:

P(X=r) = nCr × p^r × q^n-r.

Where p = probability of success

q= probability of failure.

From the given question,

n = number of samples =30,

p = Probability that a student is late = 10% = 0.1,

q=0.9

a.) when no student is late, that is when r = 0, then

P(X=0) = 30C0 × 0.1^0 × 0.9^30

P(X=0) = 0.0424 = 4.24 ≈ 4.2%

b.) when exactly one student is late, that is when r=1, then

P(X=1) = 30C1 × 0.1¹ × 0.9^29

P(X=1) = 0.1413 = 14.13 ≈ 14.1%