i. Let X be the number of students that come from a rural family out of the ten students selected. We want to find P(X < 2).
P(X < 2) = P(X = 0) + P(X = 1)
P(X = 0) = (0.55)^10 = 0.0018
P(X = 1) = 10C1 * (0.45)^1 * (0.55)^9 = 0.0276
Therefore, P(X < 2) = 0.0018 + 0.0276 = 0.0294
ii. Let Y be the number of students that come from a rural family out of the seven students selected. We want to find P(Y > 1).
P(Y > 1) = 1 - P(Y ≤ 1) = 1 - (P(Y = 0) + P(Y = 1))
P(Y = 0) = (0.55)^7 = 0.0138
P(Y = 1) = 7C1 * (0.45)^1 * (0.55)^6 = 0.0761
Therefore, P(Y > 1) = 1 - (0.0138 + 0.0761) = 0.9101
Study shows that 45% of students in SMK Cemerlang come from rural family.
i. Find the probability that less than two students come from rural family if ten students are randomly selected.
(2.5 marks)
ii. Find the probability that greater than at least one students come from rural family if seven students are randomly.
1 answer
2 answers