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Title: Probability
Description: Breaks down the little elements to understand the application of probability; furthermore, twenty-four questions included with solutions!
Description: Breaks down the little elements to understand the application of probability; furthermore, twenty-four questions included with solutions!
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GMATPREPNOW
Probability
1
...
What is the
probability that the selected number is either even or prime?
P(A) = (# of even or prime outcome) / ( total number of possible outcomes)
4/7
2
...
What is the probability that
the sum of the two numbers is 11?
P(Sum is 11) = (Number of Pairs with sum 11)/ (total number of pairs)
4/40 = 1/10
3
...
1
= 0
...
Two-‐monitor quality of an egg packaging plant, workers randomly select
eggs for testing
...
04; the
probability of selecting an extra large egg 0
...
07
...
On any given toss, the probability is 0
...
If the coin is tossed 5 times what is the probability that exactly 2 of the
tosses turn up heads?
P(2 Heads) = P(HHTTT or HTHTT or THTHT or …)
P(HHTTT) = 9/10 x 9/10 x 1/10 x 1/10 x 1/10
81/ 100,000 + 81/ 100,000 + 81/ 100,000 + …
...
A drawer contains six socks
...
Probability is less than 0
...
B
...
4 that both socks will be white
...
3 = B/6 < 0
...
33 (WRONG)
B = 1 à P(Black) = 1/6 = 0
...
4
W/6 x W-‐1/5 > 0
...
4 (Wrong)
7
...
If a point is randomly selected from the region inside
the larger circle, what is the probability that the point will be inside the
smaller circle?
Area of Small Circle / Area of Bigger Circle
π(2) ^2 / π(10)^2 = 4π/100π = 4/100 = 1/25
8
...
What is the probability that a ball
selected at random will be green ball
...
There are 15 more red balls than green balls
...
There are twice as many red balls as there are green balls
...
Box contains 12 green balls, 12 red balls, and 1 yellow ball
...
Box contains N balls, 3 of which are red
...
What is the value of N ?
P(both red) = 1/12
P(Red 1 AND Red 2) = 1/12 à Dependent, therefore P(A AND B) = P(A) x
P(B|A)
3/N x 2/N-‐1 = 1/12
N^2 – N = 72
(N-‐9) (N+8) = 0 => N= 9, -‐8
Counting
1
...
In how many ways can 6 identical coins be distributed among Alex, Bea,
and Chad? Note: Some people may receive zero coins
1st – {6,0,0}
(6 – 1)(5-‐2)(4-‐3)(3-‐4)(2-‐5)(1-‐6)(0-‐7)
nd – {5,1,0}
2
{5,0,1}
So on…
...
How many different cars are possible? If Power ( Gas, Electric, Hybrid)
then color (Red, Black, Blue) and the transmissions are (Automatic,
Standard)
TOTAL 18 Possibilities = 3 (power) x 3
(Color)x 2 (Trans)
4
...
In how many different ways can all five children be
seated in a row if the girls must sit on the end chairs?
5
...
How many positive 3 digits odd number
can be created if each number cannot contain repeated digit?
Fundamental Counting Principle = 5 x 4 x 3 = 40 total
6
...
In how many ways can the test be completed if every
question is answered?
5 x 5 x 5 x 5 = 625
7
...
If each person
finishes the race, and there are no ties
...
In how many ways can we arrange the 9 letters in the word
WONDERFUL?
9! = 362,880 ways
9
...
Chole has 3 different math books, 2 different art books and 2 different
history books
...
In how many ways can the five letters J, K, L, M, and N be arranged such
that L is not in the middle?
# of ways to follow restriction = # of ways to ignore restriction -‐ # of
ways to break restriction
Ignore = 5 x 4 x 3 x 2 x 1 = 120
Break = 4 x 3 x 1 x 2 x 1 = 24
120 – 24 = 96
12
...
In how many different ways can we arrange the 5 letters in NANNY?
N!/ (A!) (B!) (C!)
3N’s 1 A 1 Y = 5 TOTAL = n
5!/ 3! X 1! X 1! = 20
14
...
From your group of 5 friends (A, B, C, D, and E) you must select 3 friends
to join you on a campaigning trip
...
There are 50 students in a certain school
...
A certain pizza restaurant offers 12 toppings
...
How many 3-‐digit numbers greater than 399 end with 5 or 7?
1st stage (x> 3) 6 x 10 x 2 = 120 numbers
19
...
If everyone in the room shakes hands with
everyone else in the room, how many handshakes takes place?
8C2 = 8! / 2! (8-‐2)! = 28
20
...
How many different 3
toppings pizzas are possible, if the order of the 3 selected toppings does
not matter?
8C3 = 8 x 7 x 6 / 3 x 2 x 1 = 8 x 7 = 56
21
...
11C2 = 11!/ 2! X (11-‐2)! = 55
22
...
7C3 = 7!/3! X (7-‐3)! = 35
23
...
In how many different ways can the teacher select
a committee consisting of 4 students?
8C4 = 8 x 7 x 6 x 5/ 4! = 70
24
...
There are 2 red buttons, 2 blue buttons
and 2 green buttons
...
A couple is planning an evening out
...
How many different ways can they plan their evening if they
choose one of each?
4 x 5 x 3 = 60
Title: Probability
Description: Breaks down the little elements to understand the application of probability; furthermore, twenty-four questions included with solutions!
Description: Breaks down the little elements to understand the application of probability; furthermore, twenty-four questions included with solutions!