Question
Lauris records the mass and grade of 300 eggs. The table shows the results.
(a) Find the probability that an egg chosen at random is graded very large.
Answer/Explanation
Ans: \(\frac{7}{25}or\frac{84}{300}oe\)
(b) The cumulative frequency diagram shows the results from the table.
Use the cumulative frequency diagram to find
(i) the median,
Answer/Explanation
Ans: 62
(ii) the lower quartile,
Answer/Explanation
Ans: 52
(iii) the inter-quartile range,
Answer/Explanation
Ans: 19 to 20
(iv) the number of eggs with a mass greater than 65 grams.
Answer/Explanation
Ans: 125
Question
The table shows the probability that a person has blue, brown or green eyes.
| Eye colour | Blue | Brown | Green |
| Probability | 0.4 | 0.5 | 0.1 |
Use the table to work out the probability that two people, chosen at random,
(a) have blue eyes,
Answer/Explanation
Ans: 0.16 oe
(b) have different coloured eyes.
Answer/Explanation
Ans: 0.58 oe
Question
In this question, give all your answers as fractions.
A box contains 3 red pencils, 2 blue pencils and 4 green pencils.
Raj chooses 2 pencils at random, without replacement.
Calculate the probability that
(a) they are both red,
Answer/Explanation
Ans: \(\frac{1}{12}\)
(b) they are both the same colour,
Answer/Explanation
Ans: \(\frac{5}{18}\)
(c) exactly one of the two pencils is green.
Answer/Explanation
Ans: \(\frac{5}{9}\)
Question
The probability of a cricket team winning or losing in their first two matches is shown in the tree diagram.
Find the probability that the cricket team wins at least one match.
Answer/Explanation
Ans:
\(\frac{5}{6}\) oe
Question
Paul and Sammy take part in a race.
The probability that Paul wins the race is \(\frac{9}{35}.\)
The probability that Sammy wins the race is 26%.
Who is more likely to win the race?
Give a reason for your answer.
Answer/Explanation
Ans: Sammy
and
correct reason with 25.7% oe shown
Question
Simon has two boxes of cards.
In one box, each card has one shape drawn on it that is either a triangle or a square.
In the other box, each card is coloured either red or blue.
Simon picks a card from each box at random.
The probability of picking a triangle card is t.
The probability of picking a red card is r.
Complete the table for the cards that Simon picks, writing each probability in terms of r and t.
| Event | Probability |
| Triangle and red | |
| Square and red | (1 – r)r |
| Triangle and blue | |
| Square and blue |
Answer/Explanation
Ans:
| rt |
| (1-t)r |
| (1-r)t oe |
| (1-r)(1-t) e |
Question
A car of length 4.3m is travelling at 105 km/h.
It passes over a bridge of length 36m.
Calculate the time, in seconds, it takes to pass over the bridge completely.
……………………………. s
Answer/Explanation
Ans:
1.38 or 1.381 to 1.382
Question
Samira and Sonia each have a bag containing 20 sweets.
In each bag, there are 5 red, 6 green and 9 yellow sweets.
(a) Samira chooses one sweet at random from her bag.
Write down the probability that she chooses a yellow sweet.
……………………………………………
(b) Sonia chooses two sweets at random, without replacement, from her bag.
(i) Show that the probability that she chooses two green sweets is \(\frac{3}{38}\)
(ii) Calculate the probability that the sweets she chooses are not both the same colour.
Answer/Explanation
(a)\(\frac{9}{20}\)
(b)(i)\(\frac{6}{20}\times \frac{5}{19}\)
\(\frac{30}{380}\)
(ii)\(\frac{258}{380}\)
Question
The diagram shows five cards.
Two of the cards are taken at random, without replacement.
Find the probability that both cards show an even number.[2]
Answer/Explanation
Ans:
11 \(\frac{2}{20}\)oe
Question
The probability that the school bus is late is \(\frac{9}{10}\).
If the school bus is late, the probability that Seb travels on the bus is \(\frac{15}{16}\).
If the school bus is on time, the probability that Seb travels on the bus is \(\frac{3}{4}\).
Find the probability that Seb travels on the bus. [3]
Answer/Explanation
Ans:
20 \(\frac{147}{160}\) oe
Question
The probability that a sweet made in a factory is the wrong shape is 0.0028 .
One day, the factory makes 25000 sweets.
Calculate the number of sweets that are expected to be the wrong shape.[2]
Answer/Explanation
Ans:
6 70
Question
A bag contains blue, red, yellow and green balls only.
A ball is taken from the bag at random.
The table shows some information about the probabilities.
(a) Complete the table.
(b) Abdul takes a ball at random and replaces it in the bag.
He does this 200 times.
Find how many times he expects to take a red ball.
………………………………………….
Answer/Explanation
(a)0.22
(b) 40
Question
In a flu epidemic 45% of people have a sore throat.
If a person has a sore throat the probability of not having flu is 0.4.
If a person does not have a sore throat the probability of having flu is 0.2.
Answer/Explanation
P(Sore throat)\(\times 0.6\)+P(No sore throat)\(\times 0.2\)
=0.45\times 0.6\)+0.55\times 0.2\)
=0.27+0.11
=0.38