Probability

1. Probability lecture chapter 14 #2 An example

2. The probability of an event is its long term relative frequency found by . . . 1- Looking at many replications(repeats) of an event 2- Deducing it from equally likely events 3- Using some other information (the catch all)

3. A few years ago M&M’s decided to add a new color and conduct a global survey. In Japan they found that 38% chose pink, 36% teal and 16% chose purple and 10% had no preference Check to see if probabilities are legitimate – check to see if all are between 0 and 1 check the “duh” rule – all add to 1 (probability assignment rule) They don’t pass the “duh” rule so create a final category.

4. What’s the probability a random respondent preferred either pink or teal? The word “either” suggest the addition rule or P(A + B). Check if disjoint. P(pink or teal) = P(pink) + P(teal) = 0.38 + 0.36 = 0.74

5. What’s the probability that 2 random respondents both picked purple? The word “both” suggest the multiplication rule or P(A and B). Check for independence. P(both purple) = P(1st picks purple) x P(2nd picks purple) = 0.16 x 0.16 = 0.0256

6. What’s the probability that out of 3 random respondents at least 1 picked purple? The words “at least 1” suggest the complement rule or P(A) = 1 – P(Ac) Check for independence. P(not purple) = 1 – P(purple) = 1 – 0.16 = 0.84 P(none picking purple)= (0.84)3 = 0.5927 P(at least 1 purple) = 1 – P(none picked purple) 1 – 0.5927 = 0.4073