Question:
- a) Find the probability that a card chosen at random from the set of cards is
- a Purple card.
- a Blue card
- a Orange or Green card
- a Purple or Blue card
- not a Blue card
- a Red card
(b) Two cards are chosen at random one after another with replacement from the set of
cards, find the probability that
- both are Orange
- both are Blue
- the first card is Purple and the second a Green
- the first card is Orange and the second Blue
- one is Blue and the other Green
- one is Orange and the other Purple
(c) Two cards are chosen at random one after another without replacement from the set
of cards, find the probability that
- both are Orange
- both are Blue
- the first card is Purple and the second a Green
- the first card is Orange and the second Blue
- one is Blue and the other Green
- one is Orange and the other Purple
(d) Three cards are drawn at random one after another without replacement from the
set of cards, find the probability that
- all are Blue
- one Green, one Purple and one Orange
Question 2 (30 marks)
- 300 students were asked if they go to school by bus or bicycle. Their responses are recorded in the table.
Would marry in the next 3 years
|
|
Bus
|
Bicycle
|
|
Boy (B)
|
28
|
102
|
|
Girl (G)
|
152
|
18
|
If one student is selected at random from these 300 students, find the probability that
- the student goes to school by bus; [2 marks]
- the student is a boy; [2 marks]
- the student is a girl who cycled to school; [2 marks]
- the student is a boy and he goes to school by bus. [2 marks]
- the student goes to school by bus given that the student is a girl.
[2 marks]
- the student is a boy given that the student goes to school by bicycle.
[2 marks]
Given that a selected student is a boy, what is the probability that he goes to school by bus? [2 marks]
Are the events selecting a 'Boy' and go to school by 'Bicycle' independent? Explain. [2 marks]
Are the events selecting a 'Girl' and go to school by 'Bus' mutually exclusive? Explain.
[2 marks]
- The probability that a student selected at random is a male is 0.48, and a student likes statistics is 0.35. The probability of a student selected at random is a female who likes statistics is 0.25.
- Construct a contingency table based on the information given above.
[4 marks]
- What is the probability that a student selected at random is a male and likes statistics; [2 marks]
- What is the probability that a student selected at random is a female and dislikes statistics. [2 marks]
- What is the probability that a student selected at random is a male or dislike statistics. [2 marks]
- What is the probability that a student selected at random is a female or dislike statistics. [2 marks]
Question 3 (30 marks)
- The bank manager expects a decline of 20% on customer fixed deposit in the current year. He introduced a scheme to monitor the decline. If the fixed deposit is heading for a decline, there is a 70% chance that the scheme will be negative. If the fixed deposit is not headed for a decline, there is 15% chance that the scheme will be negative. The manager randomly select a customer and the scheme shows negative. What is the probability that the bank will show a decline in fixed deposit? [10 marks]
- Given that 15% of the sale receipts at a departmental store is for electrical goods. If 5 receipts were selected, what is the probability that
(i) none is for electrical goods? [3 marks]
(ii) 3 are for electrical goods? [3 marks]
(iii) at least 2 are for electrical goods? [4 marks]
- A washing machine breaks down on an average of 3 times per year. Using the
Poisson probability distribution formula, find the probability that during the next year this washing machine will have
(i) exactly 2 breakdowns; [5 marks]
(ii) at most one breakdown. [5 marks]
