Answer:
a.) 4.2%
b.) 14.1%
Step-by-step 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%
