Give an example of when to use a sum rule and when to use a product rule. Given

Question

Give an example of when to use a sum rule and when to use a product rule. Given an apartment number comprised of 2 digits followed by letter A through G. How many numbers can be generated when no number has leading 0s. For example, 10A is a correct apartment number but 01A is not. Write out the steps for computing the result. You have 6 apples, 9 oranges, 3 plums, and 3 baskets to distribute the fruit. How many different fruit baskets can you create if each basket must have at least 1 apple and 1 orange?

Explanation / Answer

1. Sum rule is to be used when we want to calculate the ptobbility of occurrence of any one of mutually exclusive events.

EXAMPLE:

One card is drawn from a pck of 52 cards. What is the probability that it is a king or queen.

Let: A = drawning a king

B = drawning a queen

P(A + B)= P(A) + P(B) = 4/52 + 4/52 = 8/52 = 2/13.

Product rule is applied when we want to get the probability of occurrrence of independent events.

EXAMPLE: In two tosses of a coin, what is the probability of getting head in both?

A = head in first trial

B = head in second trial = P(AB) P(A) P(B) = 1/2 X 1/2 = 1/4

2. First digit can be done in 9 ways, 1 to 9, since 0 is not allowed.

2nd digit can be done in 10 ways.

3rd letter can be done in 26 ways

So, total numbers = 9 X 10 X 26 = 2340.

3. all 3 baskets with no apple & orange:

First basket: probability of 3 plums out of 18 fruits = 3/18

Second basket: 1 plum has gne to 1st basket. So, Probability of 2 plums out of 17 fruits = 2/17

Third basket: Probability of 1 plum out of 16 fruits = 1/16.

So, Probability of no apple and no orange = 3/18 X 2/17 X 1/16 = 0.0033

So, Probability of at lleast 1 ap0ple and 1 orange in each basket = 1 - 0.0033 = 0.9967

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