Probability

Question 1

Probability formula of event A or B occurring when A and B can both occur at the same time.

Example question:

If a number is to be selected at random from the numbers 1 - 50, inclusive, what is the probability that the number selected will be a perfect cube or an even number?

Answer 1

P(A or B) = P(A) + P(B) - P(A and B)

P(A or B) = P(25/50) + P(3/50) - P(1/50)

25/50 = number of even numbers
3/50 = number of perfect cubes
1/50 = even number that is a perfect cube

Question 2

How to find probability for multiple outcomes

Answer 2

number of events * probability of one outcome

1. find the number of events for the ‘pot’ using the permutation formula. if repeating items, use N!/x! where x is the number of repeating items
2. determine the probability all outcomes with the pot and larger group
3. multiply the number of events by the probability of outcomes

Question 3

how to solve ‘at least’ probability questions

Answer 3

1. define the scenarios where the probability is successful at a minimum ‘at least’, and where probability is maxed/met for all events.
2. calculate the probability for each scenario. for scenario where repeating items amongst a group of items that are not identical, use permutation formula N!/x! where x is the number of repeating items to find the number of events. from there, determine probability and multiply. find probability of scenario where items are identity separately.
3. add the probability of both scenarios.

Question 4

how to solve ‘at least one’ probability questions

SHOULD ONLY DO WHEN EVENTS ARE COMPLEMENTARY

Answer 4

When a question asks for the probability that “at least 1” outcome will occur, consider using complementary events to simplify the problem. That is, P(at least 1 outcome occurs) = 1 - P(none of these outcomes occur)

Question 5

When asked the probability that some number of items will be selected, we can use combinations to determine the following

Answer 5

of ways that some number of items must be selected [use cominator formula and restrict group, subgroup] / # of ways that all items must be selected

Question 6

When asked the probability that some number of items must not be selected, we can use combinations to determine the following

Answer 6

of ways that some number of items must not be selected [use cominator formula and restrict items that must not be selected in the main group] / # of ways that all items must be selected

Question 7

When asked the probaility that some items must be selected AND some items must not be selected

Answer 7

for items that must be selected, remove them from the subgroup and larger group

for items that must not be selected, restrict them from main group

divide the probability over the # of ways that all items must be selected

Question 8

Probability of mutually exclusive events

Answer 8

1 = P(A) + P(B) - P(Both A and B) + P(Neither)

Question 9

Probability of non-mutually exclusive events

Answer 9

1 = P(A)+ P(B) + P(Both A and B) + P(Neither A or B)