A box for a school stationery order contains 30 pens, of which 4 are defective and do not write. Two pens are selected at random from the box, without repla...
Question 1 Report
A box for a school stationery order contains 30 pens, of which 4 are defective and do not write. Two pens are selected at random from the box, without replacement, for a quality check. Work out the probability that both selected pens work correctly. (3)
Answer Details
Choosing two pens without replacement means the second probability depends on what was removed first; multiplying the two conditional probabilities along the "both work" branch gives the required probability.
26 of the 30 pens work correctly, so \(P(\text{1st works}) = \dfrac{26}{30}\). [1 mark]
Given the first worked, 25 working pens remain out of 29, so \(P(\text{2nd works}\mid\text{1st works}) = \dfrac{25}{29}\). [1 mark]
Multiplying along the branch: \(P(\text{both work}) = \dfrac{26}{30}\times\dfrac{25}{29} = \dfrac{650}{870} = \dfrac{65}{87}\). [1 mark]
Download The App On Google Playstore
Everything you need to excel in your exams
