Handling Data 7
3 marks · NormalA box contains 5 pens: 3 blue and 2 black. Two pens are taken at random, one after the other, without replacement.
Work out the probability that both pens are black.
Work this out on paper, then compare with the answer and worked solution below. With a free account you can submit written answers for marking.
Show answer
0.1 (±0.01)
Also accept: 1/10
Common mistakes: Using with replacement method 0.08
Show mark scheme and worked solution
Marking points
M1 · 1 mark · States probability first pen is black: 2/5.
M2 · 1 mark · States probability second pen is black if first was black: 1/4.
A1 · 1 mark · Multiplies: 2/5 × 1/4 = 2/20 = 1/10 = 0.1.
Worked solution
First pen black: 2/5
Second pen black (one less, total now 4): 1/4