GMAT Prep Now: Probability Module (All Videos)

Video 16 Lesson: Guessing Strategies

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the probability of an event ranges from _ to _ (numbers)

0 to 1 0 = an event will never occur 1 = an event will definitely occur

For questions that may involve the complement, consider any answer choice that combines with another answer choice to add to _

1 0.6 doesn't add to 1 with any other answer

Video 4 Question: At least 1 even number If 2 numbers are randomly selected from the set {2, 3, 4, 5, 6} without replacement, what is the probability that the selection contains at least one number? A) 0.4 B) 0.64 C) 0.75 D) 0.8 E) 0.9

1-0.1 = 0.9 E.

Entire GMAT Probability Strategy process

1. Consider using the complement 2. Determine the general approach - Basic probability formula - Probability Rules 3. Basic probability formula - Equally likely outcomes? - List or use counting techniques 4. Probability rules - Rewrite question by asking, "What must occur?" - "or" probability -> test for mutually exclusivity - "and" probability -> test for independence

{-4, -3, -2, -1, 1, 2, 3} If two numbers are randomly selected, without replacement, from the above set, what is the probability that the product of the two selected numbers will be positive? P(product is positive) = _____

1. What must occur to get a positive product? 2. What must occur for both numbers to have the same sign - Both positive or both negative (- plus - = positive)

Let's say there are 2 green balls and 6 red balls. What's the probability of picking out a green ball?

2/8 = 1/4

Video 15 Question: Listing vs Counting vs Probability Rules

:-D

Video 8 Question: Red or Green Ball A box contains several balls. Each ball is a solid color. If the probability of randomly selecting a green ball is 0.6, what is the probability of randomly selecting a ball that is either green or red? 1) the probability of selecting a red ball is greater than or equal to 0.4. 2) the probability of selecting a white ball is less than or equal to 0.4

A.

video 13: rewriting questions

Around the fur

How can you determine if an event is independent or not?

Ask this question Does the occurrence of one event affect the probability of the other? Yes = dependent No = independent

Video 17 Question: Green Ball A box contains green balls and red balls only. What is the probability that a ball selected at random will be a green ball? 1) There are 15 more red balls than green balls. 2) There are twice as many red balls as there are green balls

B.

Video 10 Question: 2nd Ball is Yellow A box contains 12 green balls, 12 red balls, and a 1 yellow ball. If two balls are randomly selected one after the other without replacement, what is the probability that the second ball selected will be yellow? A) 1/600 B) 24/625 C) 1/25 D) 1/24 E) 49/600

C.

Video 20 Question: Same Color A box contains 4 green balls, 3 red balls, and 2 yellow balls. If 2 balls are randomly selected from the box without replacement, what is the probability that the 2 balls will be the same color? A) 2/9 B) 20/81 C) 5/18 D) 1/3 E) 5/12

Can the events occur together = No P(G₁G₂) = P(G₁ and G₂) Probability of selecting green and green Does the occurence of one event affect the probability of the other? - Answer = yes P(A and B) = P(A) x P(B|A) P(G₁) x P(G₂|G₁) 4/9 x 3/8 = 12/72 72 outcomes Answer = C.

If 2/7 balls are green, then what's the probability of the balls that aren't green?

Complement of selecting = not selecting When x occurs = the complement doesn't occur

Video 14 Question: Total Number of Balls A box contains N balls, 3 of which are white. If 2 balls are randomly selected without replacement, the probability is 1/12 that the 2 balls will be white. What is the value of N? A) 4 B) 6 C) 8 D) 9 E) 12

D)

Video 2 Question: Sum of 11 If a number is randomly selected from the set {1, 2, 4, 6, 7} and a number is randomly selected from the set {2, 3, 4, 5, 6, 7, 8, 9}, what is the probability that the sum of two numbers is 11? A) 1/20 B) 1/16 C) 1/12 D) 1/10 E) 1/8

D. 1/10

True or False? You should determine the numerator before the denominator in a probability question.

False Calculating the denominator first will often help you gain insight into a question

How to guess more effectively

Imagine that you are creating a difficult probability question

Example of using your instinct The probability is 0.3 that an "unfair" coin will turn up tails on any given toss. If the coin is tossed 3 times, what is the probability that at least on of the tosses will turn up tails? A) 0.027 B) 0.343 C) 0.657 D) 0.9 E) 0.973

Narrow to just 2 items.

Select one number from {2, 4, 6, 7, 9, 10, 15} Event A: Selected number is odd Event B: Selected number is less than 5 Can both events occur together?

P(A and B) = probability of both occurring (which will be 0)

If a number is randomly selected from the set {2, 3, 6, 7, 8, 9, 15}, what is the probability that the selected number is either odd or prime? Event A: Selected Number is odd Event B: Selected Number is prime

P(A) = 4/7 P(B) = 3/7 P(A and B) = 2/7

P(A AND B) =

P(A) x P(B|A)

The probability is 1/2 that a certain coin will turn up heads when tossed. If a coin is tossed two times, what is the probability that at least 1 toss turns up heads?

P(at least 1 heads) = P( 1 heads or 2 heads) At least complement = 1 - P(NOT at least 1 heads) Not at least 1 heads = 0 heads - What must occur in order to get 0 heads

Video 9 Lesson: Probability of Event A AND Event B

Pink Maggit

3 red ball example

Probability that a ball will be green = zero Probability that the ball is red = 1

Probability definition

The probability of an event = the likelihood that the event will occur

{2, 3} {5, 8, 12, 18, 20} {4, 6, 9, 10} If one number is randomly selected from each of the following three sets, what is the probability that the product of the three numbers will be even?

There's only one way in which the product may be odd. odd x odd x odd (remember, odd x even = even) Therefore, there's only 1 outcome 1 - 1/40 = 39/40 if the three of the following numbers are even

True or False Probability of the even happening + Probability of the event not happening = 1

True

Mutually Exclusive Events

Two events are mutually exclusive if both events cannot occur together

1st guessing strategy

Use your instinct

Summary of video 9

Useful for questions that requires the occurrence of two or more events

Answer of question 1

We can't draw a conclusion, because event B depends on event A

Video 3 Lesson: The Complement

White Pony

One person is randomly selected from Earth Event A: Person's age is greater than 30 years Event B: Person's age is greater than 40 years Can both events occur together?

Yes a 60 year old fits both cirteria

Video 6 Lesson: Probability of Event A OR Event B

iii

If a number is randomly selected from the set {2, 3, 6, 7, 8, 9, 15}, what is the probability that the selected number is either odd or prime? The word "or" is assumed to be _____

inclusive