# Probability Revision

**Probability revision**

Test 11/9/2014

Name:______

1A survey of class of 28 Year 9 students found that 13 like Probability and 19 like Statistics. Seven students like both Probability and Statistics and 3 like neither Probability nor Statistics.

aUse the space provided to construct a Venn diagram to represent the survey results.

bHow many students:

ido not like Statistics?

______

iilike only Probability?

______

cIf one of the 28 students was randomly selected, find:

iPr(like Probability and Statistics)

______

iiPr(like neither Probability nor Statistics)

______

2A number is chosen from the set of integers between 1 and 10 inclusive. If A is the set of odd numbers between 1 and 10 inclusive and B is the set of multiples of 3 between 1 and 10 inclusive:

aList the following sets.

iThe sample space

______

iiA

______

iiiB

______

bDraw a Venn diagram.

clist the sets:

iA BiiA B

______

iiiA′ivB only

______

dFind:

in(A)iiPr(A)

______

iiin(A B)ivPr(A B)

______

3A number is chosen from the set of positive integers between 1 and 10 inclusive.

A is the set of integers less than 5 and B is the set of even numbers between 1 and 10 inclusive.

aRepresent the two events A and B in a Venn diagram.

bList the following sets:

iA B______

iiAB______

cIf a number from the first 10 positive integers is randomly selected, find the probability that the following events occur.

iA______

iiA B______

iiiAB______

4Two people are selected without replacement from a group of four: Adam (A), Brenda (B), Caroline (C) and Darren (D).

aList all the possible combinations for the selection by completing the following table.

1stA / B / C / D

2nd / A / × / (B, A)

B / (A, B) / ×

C / ×

D / ×

bFind the probability that the selection will contain Adam and Caroline.

cFind the probability that the selection will contain Brenda.

5Consider the following Venn diagram displaying the number of elements belonging to the events A and B.

Find the following probabilities:

aPr(A)bPr(AB)

______

cPr(A/B)dPr(B /A)

______

6 From the 20 members of a ski club, 16 like skiing, 12 like snowboarding and 8 like

both skiing and snowboarding. A ski club member is chosen at random. Let A be the event ‘the person likes skiing’ and B be the event ‘the person likes snowboarding’.

aRepresent the information in a two-way table.

A / A′B

B′

bFind the probability that the person only likes snowboarding.

______

cFind the probability that the person likes snowboarding given that they like skiing.

______

dFind the probability that the person likes skiing given that they like

snowboarding.

7A bag contains 3 red (R) and 4 white (W) marbles and two marbles are selected without replacement.

aDraw a tree diagram showing all outcomes and probabilities.

bFind the probability of selecting:

ia red marble and then a white marble______

ii2 red marbles______

iii exactly 1 red marble______

8 Boxes A and B contain 4 counters each. Box A contains 2 red and 2 yellow counters and box B contains 3 red and 1 yellow counters. A box is chosen at random and then a single counter is selected.

aFind the probability of selecting a red counter from:

ibox Aiibox B

______

bRepresent the options available as a tree diagram that shows all possible outcomes and related probabilities.

cWhat is the probability of selecting box B and a red counter?

______

______

dWhat is the probability of selecting a red counter?

______

______