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?
______
______