What Is The Probability Of Drawing A Queen Or A Diamond From A Deck Of Cards? (With One Pick)

Probability Questions with Solutions

Tutorial on finding the probability of an event. In what follows, S is the sample space of the experiment in question and E is the event of interest. north(S) is the number of elements in the sample space South and n(Eastward) is the number of elements in the event East.

Questions and their Solutions

Question 1

A die is rolled, notice the probability that an even number is obtained. Solution to Question 1
Let us offset write the sample infinite S of the experiment.
Southward = {1,ii,iii,4,5,6}
Let E exist the event "an even number is obtained" and write it down.
E = {2,iv,half-dozen}
We now use the formula of the classical probability.
P(E) = n(Due east) / due north(S) = 3 / vi = 1 / two

Question ii

Ii coins are tossed, find the probability that two heads are obtained. Note: Each coin has 2 possible outcomes H (heads) and T (Tails). Solution to Question 2
The sample space S is given by.
South = {(H,T),(H,H),(T,H),(T,T)}
Let E be the event "two heads are obtained".
East = {(H,H)}
We apply the formula of the classical probability.
P(East) = n(Due east) / n(S) = ane / 4

Question iii

Which of these numbers cannot be a probability?
a) -0.00001
b) 0.5
c) one.001
d) 0
due east) one
f) 20% Solution to Question 3
A probability is always greater than or equal to 0 and less than or equal to i, hence only a) and c) above cannot stand for probabilities: -0.00010 is less than 0 and one.001 is greater than 1.

Question four

2 dice are rolled, find the probability that the sum is
a) equal to 1
b) equal to four
c) less than 13 Solution to Question 4
a) The sample space S of ii dice is shown below.
South = { (1,ane),(1,ii),(1,3),(ane,four),(1,5),(ane,half dozen)
(ii,one),(2,2),(2,three),(2,four),(ii,5),(2,6)
(3,ane),(three,2),(3,iii),(3,4),(iii,5),(iii,6)
(4,1),(4,2),(4,3),(4,4),(4,5),(4,half dozen)
(5,1),(v,2),(5,3),(5,4),(five,five),(5,6)
(six,i),(6,2),(6,three),(half dozen,4),(half dozen,5),(six,half-dozen) }
Allow Due east exist the event "sum equal to 1". There are no outcomes which correspond to a sum equal to 1, hence
P(E) = north(E) / northward(Due south) = 0 / 36 = 0
b) Three possible outcomes requite a sum equal to iv: East = {(1,iii),(2,ii),(iii,1)}, hence.
P(E) = n(E) / north(S) = 3 / 36 = one / 12
c) All possible outcomes, East = South, give a sum less than thirteen, hence.
P(E) = n(E) / north(S) = 36 / 36 = 1

Question 5

A die is rolled and a money is tossed, find the probability that the die shows an odd number and the coin shows a head. Solution to Question 5
Permit H exist the caput and T be the tail of the money. The sample space South of the experiment described in question v is as follows
S = { (1,H),(2,H),(3,H),(4,H),(5,H),(6,H)
(1,T),(2,T),(3,T),(4,T),(5,T),(six,T)}
Let E be the event "the die shows an odd number and the coin shows a head". Event E may be described every bit follows
E={(1,H),(iii,H),(5,H)}
The probability P(E) is given by
P(Due east) = due north(Due east) / northward(Due south) = 3 / 12 = i / four

Question 6

A card is drawn at random from a deck of cards. Find the probability of getting the iii of diamond. Solution to Question 6
The sample space South of the experiment in question vi is shwon below

Allow E be the event "getting the 3 of diamond". An test of the sample space shows that in that location is one "3 of diamond" so that n(E) = 1 and n(S) = 52. Hence the probability of event Eastward occurring is given by
P(E) = i / 52

Question 7

A card is drawn at random from a deck of cards. Find the probability of getting a queen. Solution to Question 7
The sample space S of the experiment in question 7 is shwon above (see question vi)
Let E be the event "getting a Queen". An test of the sample space shows that there are four "Queens" and then that due north(Eastward) = four and north(Southward) = 52. Hence the probability of event Eastward occurring is given by
P(E) = iv / 52 = ane / 13

Question 8

A jar contains iii ruddy marbles, seven greenish marbles and 10 white marbles. If a marble is drawn from the jar at random, what is the probability that this marble is white? Solution to Question 8
Nosotros offset construct a table of frequencies that gives the marbles color distributions as follows

color	frequency
cherry	3
light-green	7
white	10

We now utilise the empirical formula of the probability
P(Due east) = Frequency for white color / Total frequencies in the higher up table
= 10 / 20 = 1 / 2

Question nine

The blood groups of 200 people is distributed every bit follows: 50 have type A blood, 65 have B blood type, lxx have O claret blazon and 15 take type AB blood. If a person from this grouping is selected at random, what is the probability that this person has O claret type? Solution to Question 9
We construct a table of frequencies for the the blood groups every bit follows

group	frequency
a	fifty
B	65
O	70
AB	15

We use the empirical formula of the probability
P(E) = Frequency for O claret / Full frequencies
= lxx / 200 = 0.35

Exercises

a) A die is rolled, detect the probability that the number obtained is greater than iv.
b) Two coins are tossed, discover the probability that one

head

simply is obtained.
c) Two dice are rolled, find the probability that the sum is equal to 5.
d) A bill of fare is drawn at random from a deck of cards. Discover the probability of getting the Male monarch of heart.

Answers to higher up exercises

a) 2 / 6 = 1 / 3
b) 2 / four = 1 / 2
c) four / 36 = ane / 9
d) 1 / 52

More References and links

elementary statistics and probabilities .
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