4400 Higher June 2010 Paper 3 Q19

EdexcelHigherOld spec5 marksMultiple Events

Six coins: one 5 cent, two 10 cent and three 20 cent coins

Ashok has six coins in his pocket.
He has one 5 cent coin, two 10 cent coins and three 20 cent coins.
He takes at random a coin from his pocket.
He records its value and puts the coin back into his pocket.
He then takes at random a second coin from his pocket and records its value.

(a) Calculate the probability that he takes two 20 cent coins. (2)

(b) Calculate the probability that the second coin he takes has a higher value than the first coin he takes. (3)

Mark scheme (a)

Scheme	Marks
\(\frac{3}{6} \times \frac{3}{6}\)	M1
\(\frac{9}{36}\) or \(\frac{1}{4}\) oe	A1
	(2)

Notes

M1: for \(\frac{3}{6} \times \frac{3}{6}\) oe

A1: Sample space method – award 2 marks for a correct answer, otherwise no marks

Mark scheme (b)

Scheme	Marks
\(\frac{1}{6} \times \frac{5}{6} + \frac{2}{6} \times \frac{3}{6}\) or \(\frac{1}{6} \times \frac{2}{6} + \frac{1}{6} \times \frac{3}{6} + \frac{2}{6} \times \frac{3}{6}\) or \(\frac{3}{6} \times \frac{3}{6} + \frac{1}{6} \times \frac{2}{6}\)	M1
	M1
\(\frac{11}{36}\)	A1
	(3)
	(5 marks)

Notes

M1: for one of \(\frac{1}{6} \times \frac{5}{6}\), \(\frac{2}{6} \times \frac{3}{6}\), \(\frac{1}{6} \times \frac{2}{6}\), \(\frac{1}{6} \times \frac{3}{6}\), \(\frac{3}{6} \times \frac{3}{6}\)

M1: for sum of 2 or 3 products which, evaluated accurately, gives the correct answer

A1: Sample space method – award 3 marks for a correct answer, otherwise no marks.
Accept \(0.30\dot{5}\), 0.30, 0.31, 0.305, 0.306 etc but not 0.3

SC M1 for one of \(\frac{1}{6} \times \frac{2}{5}\), \(\frac{1}{6} \times \frac{3}{5}\), \(\frac{2}{6} \times \frac{3}{5}\)
M1 for \(\frac{1}{6} + \frac{2}{6} \times \frac{3}{5}\) or \(\frac{1}{6} \times \frac{2}{5} + \frac{1}{6} \times \frac{3}{5} + \frac{2}{6} \times \frac{3}{5}\)