Intermediate June 2022 Unit 1 Q6
6.
(a) A bag contains red balls, green balls and yellow balls.
The number of green balls is equal to the number of yellow balls.
Mali picks one ball from the bag at random.
The probability that she will pick a red ball is 0·3.
Find the probability that Mali will pick a yellow ball. [2]
The number of green balls is equal to the number of yellow balls.
Mali picks one ball from the bag at random.
The probability that she will pick a red ball is 0·3.
Find the probability that Mali will pick a yellow ball. [2]
(b) A different bag contains 10 balls.
Some of the balls in the bag are blue.
All the other balls are white.
Morgan picks a ball from the bag at random.
He says,
Some of the balls in the bag are blue.
All the other balls are white.
Morgan picks a ball from the bag at random.
He says,
“The probability that I will pick a blue ball from the bag is 0·25.”
Explain why Morgan cannot be correct. [1]| Scheme | Marks | Comments |
|---|---|---|
| (P(green or yellow) =) 0·7 or equivalent | B1 | |
| (P(yellow) = ) 0·35 or equivalent ISW | B1 | FT ‘their 0·7’ ÷ 2, provided not 0·3 and less than 1. If no marks awarded, award SC1 for P(red) + P(green) + P(yellow) = 1. |
| Scheme | Marks | Comments |
|---|---|---|
| Any valid explanation e.g. “as there are 10 balls, the only possible probabilities are 0·1, 0·2, 0·3 etc” “(you can’t have) 2·5 balls” “a quarter of 10 is not a whole number” “0·25 of 10 = 2·5, you can’t have half a ball” “10 is not divisible by 4” | E1 | Accept “you can’t have half a ball”. Allow sight of 2·5 for E1. Do not accept incomplete explanations e.g. “we don’t know how many blue (or white) balls there are”. |