CSE 230 Assignment 2

CSE 230 Assignment 2
Total Marks: 60
1. (3 marks) In a class, there are 12 male students and 10 female students. If 5 students are
selected at random from section X, what is the probability that at most 3 females are
selected?
2. Two of 10 marbles, labeled from 1 to 10, are picked from a bag without replacement.
a. (2 marks) Write down the sample space of this experiment using the set builder
method.
b. (3 marks) What is the probability that the number on the second ball is smaller than
the number on the first?
c. (3 marks) What is the probability that the number on one ball is even and the other is
odd.
3. Natasha loves to collect marbles of different colors. She has a jar where she stores all her
marbles. In that jar she has 5 red marbles, 6 blue marbles and 8 purple marbles. If she
pulls 3 marbles, what is the probability:
a. (2 marks) that the marbles picked, without replacement, are in the order purple,
red and blue?
b. (2 marks) that the marbles picked, with replacement, are all purple in color?
4. (3 marks) A Coin is thrown 3 times .What is the probability that at least one head is
obtained?
5. (3 marks) 9 students are seated at random in 3 rows of 3 desks. Let, A= “Anu and Mumu
sit in the same row” and B = “Anu and Mumu sit at one of the four corner desks”. Are A
and B independent?
6. (3 marks) In a room full of 15 people, what is the probability that at least 2 people have
the same birthday? Assume that all birthdays are equally likely (uniform distribution)
and there are 365 days in the year.
7. (3 marks) How many children should a family plan to have so that the probability of
having at least one child of each gender is at least 0.86?
8. In Bangladesh, 40% of male smokers smoke cigars. In a sample of size 20 male smokers,
what is the probability that
a. (2 mark) Exactly 4 of them smoke cigars?
b. (2 marks) At most 3 smoke cigars?
c. (2 marks) At least 3 smoke cigars?
d. (3 marks) What is the Expected value, Variance and Standard Deviation of the
above random variable?
9. (4 marks) In a recent poll, 23% of the respondents supported candidate A, 19%
supported candidate B, 13% supported candidate C, and 45% were undecided. Then 10
people are chosen at random. What is the probability that 3 people support candidate A,
4 support candidate B, 1 support candidate C and 2 are undecided?
10. 14% of the vehicles driven on a bridge are SUVs. Richard, a toll collector, counts the
number of vehicles until the first SUV crosses him. What is the probability he counts:
a. (3 marks) At most 3 vehicles
b. (3 marks) At least 4 vehicles
11. Customers arrive at a local store at a rate of 10 per hour.
a. What is the probability that, in any 2.5 hour period, the number of customers arriving
is: (i) (2 marks) exactly 15
(ii) (3 marks) at least 10
b. (3 marks) A customer arrives at the local store at 3:35pm. What is the probability that
the next customer arrives before 7:40pm?
12. (6 marks) In a sample space of 175 left handed batsmen (LHB) and 200 right handed
batsmen (RHB), it is assumed that 0.5% of all LHB and 0.4% of all RHB have trouble
playing in-swinger delivery. What is the probability that exactly 1 batsman in the sample
space faces difficulty playing an in-swinger?