Probability
How many sample points are there when tossing a die 5 times?
6^5=7776 sample points
A store has 6 different types of shirts 5 different types of pants and 3 different types of hats. In how many different combinations a costumer can purchase a shirt, a pant and a hat?
6*5*3= 90 different ways
What are the two conditions must satisfy for a valid probability distribution?
Sum (P(X))=1 and Each of P(X) must be between 0 to 1.
Four dice are tossed find the probability that all are number four.
1/1296
Which formula do we use when two events are mutually exclusive?
(a) P(A or B)=P(A)- P(B)
(b) P(A or B)=P(A)+P(B)- P(A and B)
(c) P(A or B)=P(A)+P(B)
(d) P(A and B)=P(A). P(B|A)
(e) P(A and B)= P(A). P(B)
c
Out of 5 different letters A,B,C,D,E if we want to arrange three in order. In how many different ways can we do this?
Since order is important this is permutation. 5P3= 5!/(5-3)! =120/2=60 different ways.
The normal distribution curve is bell-shaped. True or false
True
On a multiple-choice quiz with five possible answers for each question, find the probability of answering a question correctly if we make a random guess.
1/5=20%
A family has three children find the probability that they have at least one girl assume that girls and boys are equally likely in the family.
7/8=0.875=87.5%
There are 8 people in a room. We would like to select 5 to make a committee. In how many different ways can it be done?
Since order is not important this is combination. 8C5=56 different ways.
The normal curve is symmetric about the mean. True or false
True
Find the probability of getting four cards are drawn from an ordinary deck with replacement. Find the probability that all are jacks.
(4/52)*(4/52)*(4/52)*(4/52)=0.000035
Which formula do you use when two events are independent?
(a) P(A or B)=P(A)- P(B)
(b) P(A and B)= P(A). P(B)
(c) P(A or B)=P(A)+P(B)- P(A and B)
(d) P(A or B)=P(A)+P(B)
(e) P(A and B)=P(A). P(B|A)
B
In the Pennsylvania Match 6 Lotto, winning the jackpot requires that we select 6 different numbers from 1 to 49. (order is not important). In how many different ways can we select 6 number from 1 to 49?
49C6=13,983,816 different ways.
Find the value of K in the following probability distribution. P(X)=0.12,0.24,0.12,K,0.24.
0.28
Getting an Jack, a King and a Queen in this order
(4/52) . (4/51). (4/50) = 64/132600 = 0.00048265
Which formula do you use when two events are independent?
P(B|A) = 1
P(B|A) = P(A). P(B)
P(B|A) = 0
P(B|A) = P(B)
P(B|A) = P(A)
D
There are 20 women and 15 men. A committee of 6 women and 7 men is to be chosen. How many different ways can this be done?
Since order is not important. Total possible ways=20C6*15C7=249,420,600
In a multiple-choice test there are 25 questions with five choices on each question. If a student guesses on each question how many questions he is expected to get correct? Find the mean and standard deviation.
Given n=25 and p=0.2, mean=expectation=n*p=5
Var() = n*p*q
SD= 2
Find the probability of getting a club, a spade and a heart in this order.
(13/52) .(13/51). (13/50) = 2197/132600 = 0.0165686