Foundation June 2018 Paper 2 Q14

EdexcelCurrent spec4 marksBasic Probability Multiple Events

14 Javier has two sets of cards.
Each set contains 4 cards, one marked A, one marked B, one marked C and one marked D.

Javier is going to take at random one card from each set.
The table shows all possible pairs of cards that Javier could take.

		Set 2
		A	B	C	D
Set 1	A	AA	AB	AC	AD
	B	BA	BB	BC	BD
	C	CA	CB	CC	CD
	D	DA	DB	DC	DD

(a) Find the probability that Javier will take at least one card marked C. (2)

Javier is going to take at random one card from each set, note the letter on each card and replace the cards.
He is going to do this a total of 80 times.

(b) Work out an estimate for the number of times that Javier will take at least one card marked C. (2)

Mark scheme (a)

Scheme	Marks
7 outcomes with at least one C	M1
\(\dfrac{7}{16}\)	A1
	(2)

Notes

M1: Identify at least 6 (with no more than 2 incorrectly identified) outcomes with at least one C or an answer of \(\dfrac{6}{16}\) or \(\dfrac{8}{16}\) or \(\dfrac{7}{n}\) where \(n \gt 7\)

A1: Or 0.4375 or 43.75%
(allow 2dp rounded or truncated)

Scheme	Marks
\(\dfrac{7}{16} \times 80\)	M1
35	A1
	(2)
	(4 marks)