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I/GCSE Mathematics Question Analysis Topic: Mathematics - Probability
Exam Question:
From a lot of 15 bulbs which include 5 defectives, a sample of 4 bulbs is drawn one by one with replacement. Find the probability distribution of number of defective bulbs. Hence find the mean of the distribution.
Answer:
For I/GCSE Mathematics, you should know:
Let X be the number of defective bulbs drawn (out of 4) i.e., 0, 1, 2, 3, 4
P(defective bulb) = 5/15 = 1/3
Therefore P(non-defective bulb) = 1 - 1/3 = 2/3
P(X = 0) =4 C0 x (2/3)4 = 16/81
P(X = 1) =4 C1 x (1/3) x (2/3)3 = 32/81
Similarly, finding the probability for X = 2, 3, 4:

Therefore, the mean is ∑xP(x) = 108/81 = 4/3.
Work hard for your I/GCSE Mathematics examination!
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