NH 2328
N.C.E.A.
LEVEL 3.6
PROBABILITY.
THE
1.
SUPERMARKET
4 CREDITS.
40
Minutes
You should show ALL working.
1.
Elizabeth is going shopping for a dessert on two occasions.
The probability that she buys a cheesecake is 0.7.
If Elizabeth buys a cheesecake, the probability that she buys ice cream is 0.6.
If she doesn’t buy a cheesecake, the probability that she buys ice cream is 0.55.
What is the probability that Elizabeth will buy ice cream on exactly one of her trips to the supermarket?
2.
Elizabeth will only walk to the supermarket if the weather is fine and not windy.
The probability of a fine day is 0.7, a windy day is 0.4, and a windy day that is not fine 0.3.
Calculate the probability that Elizabeth will walk to the supermarket?
3.
a)
The local supermarket that Elizabeth visits sells two types of dips: Taramasalata and Tzatsaki.
The Taramasalata is available 50% of the time, Tzatsaki is available 70% of the time, and both of
them are available 40% of the time.
Calculate the probability that when Elizabeth visits the supermarket she will find at least one of the
dips available?
b)
Are the events “Taramasalata available” and “Tzatsaki available” independent?
Justify your answer.
4.
Elizabeth collected information from 170 males and 180 females on whether they shopped at either of the
two local supermarkets: Foodcity and Pak ‘n Win.
She found that 170 people shopped at Foodcity, with 90 of them being male.
She also found that 180 people shopped at Pak ‘n Win, with 80 of them being male.
What is the probability that a randomly-chosen person visits Foodcity, given that the person is female?
5.
There is a 70% chance that Elizabeth will go to Foodcity on any given day of a 7-day week.
John only goes to Foodcity once a week.
If both Elizabeth and John go to Foodcity on the same day, there is a 60% chance that they will see each
other.
Calculate the probability that Elizabeth and John will see each other on Monday 16 March ?
6.
A bag of five doughnuts is to selected from 12 doughnuts, three of which are chocolate.
If the five doughnuts are selected at random from the 12, what is the probability that all three chocolate
doughnuts go in the bag?
7.
Suppose a shelf of eight fruit pies is made up of six apple pies and 2 apricot pies.
Calculate the expected number of apricot pies in a randomly selected bag of four pies.
Clearly communicate how you calculated your answer.
NH 2328
“The Supermarket”
ASSESSMENT SCHEDULE
Achievement
Criteria
Solve
straightforward
problems
involving
probability.
No
Evidence
Code
1
P(Buy ice cream on any trip)
= 0.7  0.6 + 0.3  0.55
= 0.585
P(Buy ice cream on one trip)
= 0.585  0.415 + 0.415  0.585
= 0.48555
Judgement
Sufficiency
ACHIEVEMENT
Three of
Code A
A
Or equivalent
A
Or equivalent
A
Or equivalent
A
Justification
needed.
Or equivalent
2
Achievement
Fine
0.6
Windy
0.1 0.3
P(Fine and not windy) = 0.6
3a
Tara
0.1
0.4
Tzat
0.3
P(At least one dip) = 0.8
3b
Solve
probability
problems.
P(A).P(B) = 0.5 x 0.7
= 0.035  P(AB)
 Events not independent.
4
Male
Female
Total
Food
90
80
170
Pak
80
100
180
Merit
P(Foodcity | Female) =
5
6
MERIT:
Total
170
180
350
4
9
P(See each other on Monday)
1
 0.7   0.6
7
= 0.06
P(All 3 chocolates in bag)
3
C3 9 C 2
=
12
C5
1
=
22
Achievement
plus
A M
Or equivalent
Two of
Code M
Or
A M
Or equivalent
A M
Or equivalent
Three of
Code M
Achievement
Criteria
Apply
probability
theory.
No
Evidence
2
7
P(0 Apple) =
8
2
Excellence
P(1 Apple) =
C4
C1  6 C 3
8
2
P(2 Apple) =
C0 6 C4
C4
C2 6 C2
8
C4
Code
=
=
=
Judgement
Sufficiency
15
70
EXCELLENCE:
40
70
plus
Merit
Code E
15
70
Expected number of apricot pies
15
40
15
= 0   1  2 
70
70
70
=1
AME
Justification
needed.
Or equivalent