Higher November 2019 Paper 1 Q25

25 A bag contains 8 balls.

3 are red and 5 are blue.

2 balls are taken from the bag at random without replacement.

(a) Write down the probability that there is at least 1 red ball still in the bag. [1 mark]

(b) Work out the probability that there are at least 2 red balls still in the bag. [3 marks]

Answer	Mark	Comments
1 or 100%	B1	oe fraction, decimal or percentage eg \(\dfrac{56}{56}\)

Mark scheme (b)

Answer	Mark	Comments
Alternative method 1
\(\dfrac{3}{8}\) and \(\dfrac{2}{7}\) or \(\dfrac{6}{56}\)	M1	may be seen on a tree diagram oe fraction, decimal or percentage eg \(\dfrac{3}{28}\)
\(1 - \left(\dfrac{3}{8} \times \dfrac{2}{7}\right)\) or \(1 - \dfrac{6}{56}\)	M1dep
\(\dfrac{50}{56}\)	A1	oe fraction, decimal or percentage eg \(\dfrac{25}{28}\)
Alternative method 2
\(\dfrac{5}{8}\) and \(\dfrac{4}{7}\) or \(\dfrac{20}{56}\) or \(\dfrac{5}{8}\) and \(\dfrac{3}{7}\) or \(\dfrac{3}{8}\) and \(\dfrac{5}{7}\) or \(\dfrac{15}{56}\) or \(\dfrac{30}{56}\)	M1	may be seen on a tree diagram oe fraction, decimal or percentage
\(\dfrac{5}{8} \times \dfrac{4}{7} + 2\left(\dfrac{5}{8} \times \dfrac{3}{7}\right)\) or \(\dfrac{20}{56} + 2\left(\dfrac{15}{56}\right)\) or \(\dfrac{20}{56} + \dfrac{30}{56}\)	M1dep	oe eg \(\dfrac{5}{8} \times \dfrac{4}{7} + \dfrac{5}{8} \times \dfrac{3}{7} + \dfrac{3}{8} \times \dfrac{5}{7}\)
\(\dfrac{50}{56}\)	A1	oe fraction, decimal or percentage eg \(\dfrac{25}{28}\)

Additional guidance

Condone a correct pair of fractions seen in a multiplication chain for M1
eg \(\dfrac{3}{8} \times \dfrac{2}{7} \times \dfrac{1}{6}\) or \(\dfrac{5}{8} \times \dfrac{2}{7} \times \dfrac{3}{8} \times \dfrac{4}{7}\) (includes \(\dfrac{5}{8} \times \dfrac{4}{7}\))