Hannah throws a fair coin twice, with the probabilities summarised on the tree diagram. Work out the probability that she throws two tails.
Answers
Answer:
(b)
What is the probability of obtaining two heads?
(c)
What is the probability of obtaining a head and a tail in any order?
Example 2
A red dice and a blue dice, both unbiased, are rolled at the same time. The scores on the two dice are then added together.
(a)
Use a table to show all the possible outcomes.
(b)
What is the probability of obtaining:
(i) a score of 5,
(ii) a score which is greater than 3,
(iii) a score which is an even number?
Example 3
A card is taken at random from a pack of 52 playing cards, and then replaced. A second card is then drawn at random from the pack.
Use a tree diagram to determine the probability that:
(a)
both cards are Diamonds,
(b)
at least one card is a Diamond,
(c)
exactly one card is a Diamond,
(d)
neither card is a Diamond.
Exercises
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Question 1
The faces of an unbiased dice are painted so that 2 are red, 2 are blue and 2 are yellow. The dice is rolled twice. Three of the possible outcomes are listed below:
R R R B R Y
(a)
List all 9 possible outcomes.
(b)
What is the probability that:
(i) both faces are red,
(ii) both faces are the same colour,
(iii) the faces are of different colours?
Question 2
A spinner is marked with the letters A, B, C and D, so that each letter is equally likely to be obtained. The spinner is spun twice.
(a)
List the 16 possible outcomes.
(b)
What is the probability that:
(i) A is obtained twice,
(ii) A is obtained at least once,
(iii) both letters are the same,
(iv) the letter B is not obtained at all?
Question 3
Two fair dice are renumbered so that they have the following numbers on their faces:
1, 1, 2, 3, 4, 6
The dice are rolled at the same time, and their scores added together.
(a)
Draw a table to show the 36 possible outcomes.
First Dice
Second Dice
1 1 2 3 4 6
1
1
2
3
4
6
(b)
What is the probability that the total score is:
(i) 6,
(ii) 3,
(iii) greater than 10,
(iv) less than 5 ?
Question 4
A red spinner is marked with the numbers 1 to 4 and a blue spinner is marked with the numbers 1 to 5. On each spinner all the numbers are equally likely to be obtained. The two spinners are spun at the same time and the two scores are added together.
(a)
Draw a table to show the 20 possible outcomes.
Blue Spinner
Red Spinner
1 2 3 4 5
1