1. The Binomial Distribution
Calculations on GC involving
≥ or >

2. On the GC we must always turn ≥ or > into ≤ questions
On the GC we must always turn ≥ or > into ≤ questions. Often we use the fact that complementary events have probabilities that add to one ie P(A) + P(A`) = 1 So P(A) = 1 – P(A`) Eg: If X > 4 means X is 5, 6,7 etc It has complement: X` is 4, 3 , 2, 1, or 0 = X` ≤ 4 So P(X > 4) = 1 - P(X≤ 4)
Now ok to use GC

3. Example One: In a multi-choice test, Sally guesses the answers to the last 6 questions. Each question has 5 choices. Find the probability that Sally gets 2 or more questions correct Find P(X≥2) for n=6 and p=0.2 Must always turn ≥ into ≤ questions for GC P(X≥2) means X=2,3,4,5 ,6 so the complement is X` =1 or 0 This can be written as X` ≤1 So P(X≥2) = 1- complement = 1- P(X` ≤1) = 1 – On GC go: menu 1= run 1 – shift ans =

4. Example Two
Sarah passes through seven sets of traffic lights on the way to work. The probability that she must stop at any light is a) Calculate the probability that she will have to stop at 5 or more lights. n = 7 p = 0.65 We need to find P(X≥ 5) Since ≥ we need to use the complement X is 5 , 6 or 7 X` is 4, 3, 2, 1, 0 we will use 1 – P(X` ≤4) 1 – P(X` ≤4) = 1 – =

5. Example Two continued
b) Calculate the probability that she will get 5 or more green lights Probability stopping (red light) = 0.65 So probability of green = 0.35 n = 7 p = 0.35 We need to find P(X≥ 5) Since ≥ we need to use the complement X is 5 , 6 or 7 X` is 4, 3, 2, 1, 0 we will use 1 – P(X` ≤4) 1 – P(X` ≤4) = 1 – =

6. Summary
The only 2 options on GC so change all questions into one of these forms
Use your GC for Binomial distribution by using:
Bpd for P(X= )
Bcd for P(X≤ )
If P(X < ) change into P(X ≤ ) and use Bcd
If P(X > ) or P(X ≥ ) use the complement and change into 1 – P(X`≤ )
Write out both lists of X and it’s complement to make sure you don’t make a mistake