Quiz #13 – Probability
IB HL 2
1.
2.
Name: _____________
An advanced mathematics class consists of 8 girls and 6 boys.
(a)
How many different committees of 6 students can be chosen from this class?
(b)
How many such committees can be chosen if class members Jack and Jill cannot both be
on the committee?
(c)
How many such committees can be chosen if there must be more girls than boys on the
committee?
(d)
How many such committees can be chosen if Jill is to be the chair of the committee?
Three bags each contain colored discs as shown in the chart below.
(a)
(b)
Bag 1
Bag 2
Bag 3
White
1
2
3
Red
3
1
2
Black
2
3
1
A bag is chosen at random and two discs are selected from it without replacement.
(i)
Find the probability that two red discs are selected.
(ii)
Given that one of the discs is red and the other is white, find the probability that they came
from Bag 2.
A disc is chosen at random from Bag 1 and placed in Bag 2. The discs in Bag 2 are shaken up,
then one is withdrawn and placed in Bag 3. What is the probability that there is only one black
disc in Bag 3 now?
3.
4.
5.
Four letters are picked from the word BREAKDOWN. Find
(a)
the probability that all the letters are consonants;
(b)
the probability that there is at least one vowel among the letters;
(c)
the probability that the selection contains the letter K or D but not both.
A bag of popping corn contains 23 white kernels and
pop, whereas 23 of the yellow ones will pop.
yellow kernels. Only
1
2
of the white kernels will
(a)
A kernel is selected at random from the bag, and pops when placed in the popper. What is the
probability that the kernel selected was yellow?
(b)
Two kernels are placed in the popper, but only one pops. What is the probability they were both
yellow?
Given that P  X  
(a)
6.
1
3
P  Y  ;
2
2
1
, P  Y X   and P  Y X   find
3
5
4
(b)
P  X  Y  .
When a person needs a minicab, it is hired from one of three firms, X, Y and Z. Of the hirings, 40%
are from X, 50% are from Y and 10% are from Z. For cabs hired from X, 9% arrive late, and the
corresponding percentages for cabs hired from firms Y and Z are 6% and 20% respectively.
(a)
Calculate the probability that the next cab hired will be from X and will not arrive late.
(b)
Calculate the probability that the next cab hired will arrive late;
(c)
Calculate the probability that the next cab hired came from Y given that it arrives late.