CAMBRIDGE IGCSE MATHS (0580)
Paper 2 (P2): Probability Topic Quiz 3
Question 1:
In all parts of this question give your answer as a fraction in its lowest terms.
In all parts of this question give your answer as a fraction in its lowest terms.
(a)
(i) The probability that it will rain today is 1⁄3.
What is the probability that it will not rain today?
Answer(a)(i) ............................................... [1]
(ii) If it rains today, the probability that it will rain tomorrow is 2⁄5.
If it does not rain today, the probability that it will rain tomorrow is 1⁄6.
Complete the tree diagram.
[2]
(b) Find the probability that it will rain on at least one of these two days.
Answer(b) ............................................... [3]
(c) Find the probability that it will rain on only one of these two days.
Answer(c) ............................................... [3]
Question 2:
In this question, give all your answers as fractions.
When Ivan goes to school in winter, the probability that he wears a hat is 5⁄8.
If he wears a hat, the probability that he wears a scarf is 2⁄3.
If he does not wear a hat, the probability that he wears a scarf is 1⁄6.
In this question, give all your answers as fractions.
When Ivan goes to school in winter, the probability that he wears a hat is 5⁄8.
If he wears a hat, the probability that he wears a scarf is 2⁄3.
If he does not wear a hat, the probability that he wears a scarf is 1⁄6.
(a) Complete the tree diagram.
[3]
(b) Find the probability that Ivan
(i) does not wear a hat and does not wear a scarf,
Answer(b)(i) ............................................... [2]
(ii) wears a hat but does not wear a scarf,
Answer(b)(ii) ............................................... [2]
(iii) wears a hat or a scarf but not both.
Answer(b)(iii) ............................................... [2]
(c) If Ivan wears a hat and a scarf, the probability that he wears gloves is 7⁄10.
Calculate the probability that Ivan does not wear all three of hat, scarf and gloves.
Answer(c) ............................................... [3]
Question 3:
In a box, there are 7 red cards and 3 blue cards.
A card is drawn at random from the box and is not replaced.
A second card is then drawn at random from the box.
In a box, there are 7 red cards and 3 blue cards.
A card is drawn at random from the box and is not replaced.
A second card is then drawn at random from the box.
(a) Complete this tree diagram.
[3]
(b) Work out the probability that the two cards are of different colours.
Give your answer as a fraction.
Answer(b) ............................................... [3]
Question 4:
If the weather is fine, the probability that Carlos is late arriving at school is 1⁄10.
If the weather is not fine, the probability that he is late arriving at school is 1⁄3.
The probability that the weather is fine on any day is 3⁄4.
If the weather is fine, the probability that Carlos is late arriving at school is 1⁄10.
If the weather is not fine, the probability that he is late arriving at school is 1⁄3.
The probability that the weather is fine on any day is 3⁄4.
(a) Complete the tree diagram to show this information.
[3]
(b) In a school term of 60 days, find the number of days the weather is expected to be fine.
Answer(b) ................................................ [1]
(c) Find the probability that the weather is fine and Carlos is late arriving at school.
Answer(c) ................................................ [2]
(d) Find the probability that Carlos is not late arriving at school.
Answer(d) ................................................ [3]
(e) Find the probability that the weather is not fine on at least one day in a school week of 5 days.
Answer(e) ................................................ [2]
Question 5:
Each morning the probability that it rains is 2⁄3.
If it rains, the probability that Asha walks to school is 1⁄7.
If it does not rain, the probability that Asha walks to school is 4⁄7.
Each morning the probability that it rains is 2⁄3.
If it rains, the probability that Asha walks to school is 1⁄7.
If it does not rain, the probability that Asha walks to school is 4⁄7.
(a) Complete the tree diagram.
[2]
(b) Find the probability that it rains and Asha walks to school.
Answer(b) ................................................... [2]
(c) (i) Find the probability that Asha does not walk to school.
Answer(c)(i) ................................................... [3]
(ii) Find the expected number of days Asha does not walk to school in a term of 70 days.
Answer(c)(ii) ................................................... [2]
(d) Find the probability that it rains on exactly one morning in a school week of 5 days.
Answer(d) ................................................... [2]
Question 6:
The probability that it will rain tomorrow is 5⁄8.
If it rains, the probability that Rafael walks to school is 1⁄6.
If it does not rain, the probability that Rafael walks to school is 7⁄10.
The probability that it will rain tomorrow is 5⁄8.
If it rains, the probability that Rafael walks to school is 1⁄6.
If it does not rain, the probability that Rafael walks to school is 7⁄10.
(a) Complete the tree diagram.
[3]
(b) Calculate the probability that it will rain tomorrow and Rafael walks to school.
Answer(b) ................................................ [2]
(c) Calculate the probability that Rafael does not walk to school.
Answer(c) ................................................ [3]
Question 7:
The probability that Chaminda uses the internet on any day is 3⁄5.
The probability that Niluka uses the internet on any day is 3⁄4.
The probability that Chaminda uses the internet on any day is 3⁄5.
The probability that Niluka uses the internet on any day is 3⁄4.
(i) Complete the tree diagram.
[2]
(ii) Calculate the probability that, on any day, at least one of the two students uses the internet.
Answer(b)(ii) ............................................... [3]
(iii) Calculate the probability that Chaminda uses the internet on three consecutive days.
Answer(b)(iii) ............................................... [2]
Question 8:
Yeung and Ariven compete in a triathlon race.
The probability that Yeung finishes this race is 3⁄5.
The probability that Ariven finishes this race is 2⁄3.
Yeung and Ariven compete in a triathlon race.
The probability that Yeung finishes this race is 3⁄5.
The probability that Ariven finishes this race is 2⁄3.
(a) (i) Which of them is more likely to finish this race? Give a reason for your answer.
Answer(a)(i) ...................................................... because ..........................................................
..................................................................................................................................................... [1]
(a) (ii) Find the probability that they both finish this race.
Answer(a)(ii) ................................................ [2]
(a) (iii) Find the probability that only one of them finishes this race.
Answer(a)(iii) ................................................ [3]
(b) After the first race, Yeung competes in two further triathlon races.
(i) Complete the tree diagram.
[3]
(b) (ii) Calculate the probability that Yeung finishes all three of his races.
Answer(b)(ii) ................................................ [2]
(b) (iii) Calculate the probability that Yeung finishes at least one of his races.
Answer(b)(iii) ................................................ [3]
Question 9:
A train stops at station A and then at station B.
If the train is late at station A, the probability that it is late at station B is 0.9.
If the train is not late at station A, the probability that it is late at station B is 0.2.
The probability that the train is late at station A is 0.3.
A train stops at station A and then at station B.
If the train is late at station A, the probability that it is late at station B is 0.9.
If the train is not late at station A, the probability that it is late at station B is 0.2.
The probability that the train is late at station A is 0.3.
(a) Complete the tree diagram.
[2]
(b) (i) Find the probability that the train is late at one or both of the stations.
Answer(b)(i) ................................................ [3]
(b) (ii) This train makes 250 journeys. Find the number of journeys that the train is expected to be late at one or both of the stations.
Answer(b)(ii) ................................................ [1]
(c) The train continues to station C. The probability that it is late at all 3 stations is 0.27.
Describe briefly what this probability shows.
..............................................................................................................................................................
.............................................................................................................................................................. [1]
Question 10:
The probability that a plant will produce flowers is \( \frac{7}{8} \).
The flowers are either red or yellow.
If the plant produces flowers, the probability that the flowers are red is \( \frac{3}{4} \).
The probability that a plant will produce flowers is \( \frac{7}{8} \).
The flowers are either red or yellow.
If the plant produces flowers, the probability that the flowers are red is \( \frac{3}{4} \).
(a) (i) Complete the tree diagram by writing a probability beside each branch.
[2]
(a) (ii) Calculate the probability that a plant, chosen at random, will produce red flowers.
Answer(a)(ii): ................................................ [2]
(a) (iii) Two plants are chosen at random. Calculate the probability that both will produce red flowers.
Answer(a)(iii): ................................................ [2]
(b) Alphonse buys 200 of these plants. Calculate the number of plants that are expected to produce flowers.
Answer(b): ................................................ [2]
(c) Gabriel has 1575 plants with red flowers. Estimate the total number of plants that Gabriel has.
Answer(c): ................................................ [2]
