GMAT Quant Chapter 16: Probability Flashcards
Define complementary events.
Two events share no common outcomes but cover all possible outcomes
(link to collectively exhaustive in Chapter 15)
What is the probability formula?
The number of desired outcomes
/
The total number of possible outcomes
What is the addition rule with mutually exclusive events?
What is the addition rule with non-mutually exclusive events? What happens if you don’t account for the intersection?
P(A or B) = P(A) + P(B)
P(A or B) = P(A) + P(B) - P(A and B)
If you don’t include the intersection in the calculation with non-mutually exclusive events the probability will be overstated.
How do we determine the probability of multiple outcomes?
What must be true for us to use this shortcut?
number of possibilities * the probability of one event
When each of the outcomes has the same probability (e.g. flipping a coin)
What are the 3 steps in determining the probability of “at least” x events occurring?
Step 1: Define the scenarios
Step 2: Calculate the probability of each scenario
Step 3: Sum the probability of each scenario
What shortcut can we use to determine the probability of X events occurring?
What must we ensure?
The complementary principle.
P(A) + P(A’) = 1, P(A’) = 1 – P(A)
The principle holds. Is the probability either or.
How can we use combinatorics to determine probabilities?
The probability when some number of items must be selected:
Favourable outcomes / total outcomes =
number of ways the selection must happen
/
total number of ways the selection can happen
How should we think about probabilities in terms of ratios?
What can we use this fact to determine?
a probability is the ratio of favourable outcomes to the total number of outcomes
Probability is a fraction. Any rule that can be applied to a fraction can also be applied to a probability.
How many unique items there are in a set
Give an example of how we can express probability algebraically.
The probability of selecting a red marble from a Jar is 1/4, what is the chance of selecting two in a row without replacement?
1/4 is r/4
so the second choice is r-1/3
so the probability of both choices together is:
r/4 * r-1/3
we can then turn this into a quadratic, set it equal to a known probability, and solve for r
What do we know about the probability of two non-mutually exclusive sets?
(similar to overlapping sets)
What is another formula we can use for two non-mutually exclusive sets that include “only” subsets?
1 = P(A) + P(B) - P(both A and B) + P(neither A nor B)
1 = P(A only) + P(B only) + P(both A and B) + P(neither A nor B)
