Review Set 14A

1. Donald keeps record of the number of clients he telephones over a consecutive period of days.
a. for how many days did the survey last?
b.estimate Donald's chances of telephoning:
i) no clients in a day
ii) four or more clients on a day
iii). less than three clients on a day

a. 1+6+12+9+6+3+2=39 total number of days
b. i). 1/39
ii). 6+3+2=11/39
iii). 1+6+12=19/39
2. David conducted a survey to determine the ages of people walking through a shopping mall. the results are shown in your book. find , correct to 3 decimal places the estimated probability that the next person David meets in the shopping mall is:
a. between 20 and 39 years of age
b. less than 40 years of age
c. at least 20 years of age

a. 45/112=0.4017~0.402
b. 45+19=64/112=0.5714~0.571
c. 45+37+11/112 or 112-19/112=93/112=0.8303~0.830
3. A farmer fences his rectangular property into 9 rectangular paddocks:
If a paddock is selected at random,what is the probability that:
a. it has no fences on the boundary of the property
b. it has one fence on the boundary of the property
c. it has two fences on the boundary of the property?

a. 1/9 because all but one is on a boundary
b. 4/9
c. 4/9
4. When a box of drawing pins dropped on to the floor it was observed that 47 landed on their backs and31 landed on their sides.Find correct to 2 decimal places,the estimated probability of a drawing pin landing:
a. on its back
b. on its side

47-Back, 31-Side
78 total number of pins
a. 47/78=0.602~0.60
b. 31/78=0.397~0.40
5. A saw mill receives logs of various lengths from a plantation. the length of a log is important in being able to produce timber of the length required.the following data indicates the lengths of at least100 logs received.
a. what is the probability of a log being less than 11 metres long arriving at the saw mill?
b. What is the probability of a log being longer than 15 metres arriving at the saw mill?
c. in the next batch of 50 logs how many would be expected to be between 11 m and 15 m long?

a. L < 11=3+4+14/100=21/100
b. L > 15=7+8/100=15/100
c. 11< L < 15=12+18+20+14=64/2=32 per 50 logs
6.At peak hour railway crossings are closed 30% of the time. If you have to drive through three railway crossings during peak hour, what are the chances you will have to stop at least once?

o-open=.7, c-closed=.3
Possible combination's
ooo-.7*.7*.7=.343
ooc
occ
coo
coc
cco
ccc

1-P(ooo)
1-.343=0.657
7.In a golf match, Annette has a 70% chance of hitting the green when using a nine iron and Kari has a 90% chance when using the same club. If, at a particular hole,they both elect to use a nine iron to play to the green, determine the probability that:
a. both hit the green
b. neither hits the green
c. at least one hits the green
d. only Anette hits the green

a..7*.9=.63
b. .3*.1=.03
c. 1-P(of no one)
1-.03=.97
d. .7*.1=.07
8. Jar A contains 3 white and 2 red marbles. Jar B contains 6 white and 4 red marbles. A jar is selected at random and then two marbles are selected WITHOUT replacement. Determine the probability that:
a. both marbles are white
b. two red marbles are picked from Jar A

Jar A: 3 whites, 2 red
Jar B: 6 whites, 4 red
a. Jar A- 1/2*3/5*2/4=6/40
Jar B- 1/2*6/10*5/9=30/180
6/40+30/180=19/60 (add because they're independent)
b. 1/2*2/5*1/4=2/40

QUESTION OF THE DAY

If P(C)= .10 P(D)= .3 and P(C U D)= .11 are C and D independent events?