4MA0 Higher January 2014 Paper 3R Q8

EdexcelHigherOld spec9 marksBasic Probability Multiple Events

8 Morse Code uses dots (●) and dashes (▬) to represent each letter of the alphabet.
Here are 10 cards.
Each card has the Morse Code for a letter on it.

Ten cards with Morse Code: dot dash; dash dot dot dot; dash dot dash dot; dash dot dot; dot dot dash dot; dash dash dot; dot dot; dash dot dash; dash dash; dot dash dash dot

(a) Kelly takes at random one of the cards.
Find the probability that she takes a card with 2 dots or a card with 3 dots. (2)

(b) Hashim has the 10 cards.
He takes at random a card 200 times.
He replaces the card each time.
Work out an estimate for the number of times he will take a card with exactly 2 dots. (2)

(i) there is exactly 1 dot on each card she takes,

(ii) there is a total of 4 dots on the two cards she takes.

(5)

Scheme	Marks
\(\frac{4}{10} + \frac{2}{10}\) or 4 + 2 or 6	M1
\(\frac{6}{10}\) or \(\frac{3}{5}\)	A1
	(2)

Scheme	Marks
eg \(\frac{4}{10} \times 200\)	M1
80	A1
	(2)

Mark scheme (c)

Scheme	Marks
(i) \(\frac{3}{10} \times \frac{2}{9}\)	M1
\(\frac{6}{90}\) oe	A1
(ii) \(\frac{3}{10} \times \frac{2}{9} + \frac{4}{10} \times \frac{3}{9} + \frac{2}{10} \times \frac{3}{9}\)	M1 M1
\(\frac{24}{90}\) oe	A1
	(5)
	(9 marks)

Notes

A1: \(\frac{6}{90}\) oe inc \(\frac{1}{15}\)
SC M1 for \(\frac{3}{10} \times \frac{3}{10}\)

M1 M1: M1 for one correct product
M1 for sum of all 3 correct products

A1: for \(\frac{24}{90}\) oe inc \(\frac{4}{15}\)
SC: M1 for \(\frac{3}{10} \times \frac{2}{10}\) or \(\frac{4}{10} \times \frac{4}{10}\) or \(\frac{2}{10} \times \frac{3}{10}\)
M1 for \(\frac{3}{10} \times \frac{2}{10} + \frac{4}{10} \times \frac{4}{10} + \frac{2}{10} \times \frac{3}{10}\)