 # Revision Sheet 1.

## Presentation on theme: "Revision Sheet 1."— Presentation transcript:

Revision Sheet 1

Question 1a Two independent events A and B are such that p(A) = 0.6 and find the probability of the following events: a.

Question 1a Two independent events A and B are such that p(A) = 0.6 and find the probability of the following events: a.

Question 1b Two independent events A and B are such that p(A) = 0.6 and find the probability of the following events: b.

Question 1b Two independent events A and B are such that p(A) = 0.6 and find the probability of the following events: b.

Question 1c Two independent events A and B are such that p(A) = 0.6 and find the probability of the following events: c.

Question 1c Two independent events A and B are such that p(A) = 0.6 and find the probability of the following events: c.

Question 1d Two independent events A and B are such that p(A) = 0.6 and find the probability of the following events: d.

Question 1d Two independent events A and B are such that p(A) = 0.6 and find the probability of the following events: d.

Question using a Venn diagram
Two independent events A and B are such that p(A) = 0.6 and p(B) =0.5 A B 0.2 0.3 0.3 0.2

A B 0.2 0.3 0.3 0.2

A B 0.2 0.3 0.3 0.2

A B 0.2 0.3 0.3 0.2

A B 0.2 0.3 0.3 0.2

Question 2 A and B are two events such that and
find the probability of the following events:

Question 2 A and B are two events such that and
find the probability of the following events: The question does not say the events are independent so we calculate first.

Question 2 A and B are two events such that and
find the probability of the following events:

Question 2

Question 2- easier with a Venn diagram

A B 0.45 0.05 0.25 0.25

A B 0.45 0.05 0.25 0.25

Question 3 Urn A contains 9 cubes of which 4 are red. Urn B contains 5 cubes of which 2 are red. A cube is drawn at random and in succession from each urn. a. Draw a tree diagram representing this process. b. Find the probability that both cubes are red. c. Find the probability that only 1 cube is red. d. If only 1 cube is red, find the probability that it came from urn A.

R R R’ R R’ R’ Draw a tree diagram representing this process. 2/5 3/5
4/9 R’ R 5/9 2/5 R’ 3/5 R’

R R R’ R R’ R’ b. Find the probability that both cubes are red. 2/5
3/5 4/9 R’ R 5/9 2/5 R’ 3/5 R’

R R R’ R R’ R’ c. Find the probability that only 1 cube is red. 2/5
3/5 4/9 R’ R 5/9 2/5 R’ 3/5 R’

R R R’ R R’ R’ If only 1 cube is red, find the probability that it
came from urn A. R 2/5 R 3/5 4/9 R’ R 5/9 2/5 R’ 3/5 R’

Question 4 A box contains 5 red, 3 black and 2 white cubes. A cube is randomly drawn and its colour noted. The cube is then replaced, together with 2 more of the same colour. A second cube is then drawn. a. Find the probability that the first cube selected is red. b. Find the probability that the second cube is black. c. Given that the first cube selected was red, what is the probability that the second cube selected is black?

Question 4 A box contains 5 red, 3 black and 2 white cubes. A cube is randomly drawn and its colour noted. The cube is then replaced, together with 2 more of the same colour. A second cube is then drawn. Find the probability that the first cube selected is red. 5/10

Question 4 A box contains 5 red, 3 black and 2 white cubes. A cube is randomly drawn and its colour noted. The cube is then replaced, together with 2 more of the same colour. A second cube is then drawn. Find the probability that the second cube is black. Combinations are RB, BB, WB

Question 4 A box contains 5 red, 3 black and 2 white cubes. A cube is randomly drawn and its colour noted. The cube is then replaced, together with 2 more of the same colour. A second cube is then drawn. Given that the first cube selected was red, what is the probability that the second cube selected is black? 3/12

Question 5 A fair coin, a double-headed coin and a double-tailed coin are placed in a bag. A coin is randomly selected. The coin is then tossed. a. Draw a tree diagram showing the possible outcomes. b. Find the probability that the coin lands with a tail showing uppermost. c. In fact, the coin falls “heads”, find the probability that it is the “double-headed” coin.

Draw a tree diagram showing the possible outcomes.
1/2 fair 1/3 1/2 T H 1 1/3 head T 1/3 H tail 1 T

b. Find the probability that the coin lands with a tail showing uppermost.
1/2 fair 1/3 1/2 T H 1 1/3 head T 1/3 H tail 1 T

In fact, the coin falls “heads”, find the probability that it is the “double-headed” coin.
1/2 fair 1/3 1/2 T H 1 1/3 head T 1/3 H tail 1 T

Question 6 Two unbiased coins are tossed together. Find the probability that they both display heads given that at least one is showing a head.

Question 6 Two unbiased coins are tossed together. Find the probability that they both display heads given that at least one is showing a head. 1/3