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The Fundamental Counting Principle is also called the counting rule. It is a way to identify the number of outcomes in a probability word problem.
Probability is the chance or the occurrence of an event.
Properties of Probability
- The probability of an event is always between 0 and 1.
- If we add the sum of probabilities of all events, it is equal to 1.
- The probability that an event E will not happen is 1 minus the probability A that the event will happen. P(E)=1-P(A)
- The probability that both events A and B will happen is equal to the occurence of event A times event B given that in event B, event A has already happened.
- The probability that event A or B will occur is equal to the sum of probability of each event, minus the probability that both events A and B occured.
There are 5 different tops, 4 different skirts, 7 different shoes and 8 different hats. We can let these be:
- A = 5 tops
- B = 4 skirts
- C = 7 shoes
- D = 8 hats
We know that the formula for finding the total combinations is:
- N = A x B x C x D
- N = 5 x 4 x 7 x 8
- N = 1,120 ways
By multiplying the different clothes, we got 1,120 ways or combinations of outfits from which the girl can choose.
There are 6 cakes in the refrigerator. 2 are strawberry cakes, 3 are chocolate cakes, and 1 is a mocha cake. What is the probability of getting a strawberry cake?
We can let:
- S = strawberry cake = 2
- T = total number of cakes = 6
- P = probability of getting a strawberry cake
P = S/T = 2/6 = 1/3
- The probability of getting a strawberry cake from the refrigerator is ⅓. To understand the probability further, we can change ⅓ to 0.3333, then multiply it by 100, making it 33.33, which is 33.33%, the percentage of getting a strawberry cake from the refrigerator.
Understanding Fundamental Counting Principle and Probability of Events Worksheets
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