Download STA 2023

STA 2023
Probability
Sanchez
Assignment 1.
Name: _________________________________________
I. Two marbles are selected from a box that contains 2 red marbles, a blue marble and a
green marble.
1. If drawing is done without replacing the first marble before selecting the second
marble,
a) express in list notation the sample space that shows the color of the first ball selected
and the color of the second ball selected.
Answer
S= {RR, RB, RG, BR, BG, GR, GB }
b) express in list form the even A of the sample space in part a) which consists of a
selection of marbles of different colors.
Answer
A={_RB, RG, BR, BG, GR, GB}
c) Find the probability of event A
Answer : P( A) 
c) __6/7___________
6
7
d) What are the against event A?
d) __1 to 6 ___
Answer : odds against A are 1 to 6
___________________________________________________________________
2. If drawing is done replacing the first marble before selecting the second marble,
a) express in list notation the sample space that shows the color of the first ball selected
and the color of the second ball selected.
Answer
S= {RR, RB, RG, BB, BR, BG, GG, GR, GB }
b) express in list form the even A of the sample space in part a) which consists of a
selection of marbles of different colors.
Answer
A={_RB, RG, BR, BG, GR, GB}
c) Find the probability of event A
Answer : P( A) 
c) __2/3___________
6
2
or
9
3
d) What are the against event A?
Answer : odds against A are 1 to 2
d) __1 to 2____________
III. If a coin is tossed three times, what is the probability of obtaining two heads and a
tail?
Answer: ___3/8_______
S={HHH, HHT, HTH, THH, TTH, THT, HTT, TTT}
P(two Heads and a Tail)= 3/8
IV. If two people are selected at random from three married couples (6 people), what is
the probability that a married couple will be selected?
Answer: there are 6C2 = 15 possible selections of two people.
There are 3 married couples, therefore there are 3 favorable ways.
Probability that a married couple will be selected =3/15 = 2/5 Answer: 1/5
V. How many selections of at least one fruit are possible from 3 identical mangos, 2
identical bananas and 1 apple.
Answer: 4)(3)(2) – 1 =23
answer: 23
VI. A pair of dice (plural of die) are rolled and we observed the numbers that appear on
their top faces, that is 1, 2, 3, 4, 5, or 6. How many points are there in the sample space
which shows both numbers observed on the top faces?
Answer: (6)(6) =36
answer: 36
VII. A three volume encyclopedia is placed at random on a bookshelf. What is the
probability that the books are not placed in the correct order?
Answer: there are 3! = 6 ways of placing the books on the bookshelf, only one is the
correct way (5 are incorrect)
P(books are not placed in the correct order) = 5/6
answer: 5/6
VIII. A game consists of tossing a coin, if a head H appears the game is over. If tail T
appears you continue playing until you obtain a H. If you obtain three tails T in a row the
game is over. Find the sample space of the experiment and the probability of each point
in the sample space.
H
H
T
H
T
T (over)
Points
H
Probability 0.5
TH
0.25
TTH
0.125
TTT
0.125
IX. If the first card you draw (without replacement) from an ordinary deck of cards is a
king, what is the probability that the second card is also a king?
P( K 2 | K1 ) 
3 1

51 17
answer: 1/17
X. In a group of 40 students, 20 of them are taking Statistics and 2 of them (of the 20)
are also taking Business Calculus. 5 of the 40 students are taking neither Statistics nor
Business Calculus. How many of the 40 students are taking Business Calculus?
S
B
18
2
x
5
S: students taking statistics, B: students taking business calculus.
18 + 2 + x + 5 = 40, therefore x = 15
Therefore, there are 15+ 2 = 17 students taking business calculus.
Answer: __ 17 _________