1. The binomial distribution

2. Throwing five dice
Number of sixes 1 2 3 4 5
Tally:
Relative frequency

3. Throwing five dice What is the probability distribution?
Number of sixes 1 2 3 4 5
Probability
What is the probability distribution?

4. Tree diagram, two dice

5. Tree diagram, three dice
The probability of all the equivalent paths is the same. We multiply by the number of possible paths.

6. Two dice: Three dice: “Pascal’s triangle” Number of sixes 1 21 2
Probability
Three dice:
Number of sixes 1 2 3
Probability
“Pascal’s triangle”

7. Five dice: Four dice: Number of sixes 1 2 3 4 Probability1 2 3 4
Probability
Five dice:
Number of sixes 1 2 3 4 5
Probability

8. Probability distribution for the number of sixes in 30 throws.

9. P(no sixes, five of anything else)
Why “binomial”?
P(no sixes, five of anything else)
P(five sixes)

10. X = the result of the experiment (number of successes)
r = a number in the range 0 to n
n = number of trials
p = probability of each “success”
q = 1-p = probability of each “failure”

12. Success or failure?
With 5 dice if just two are a “six”, the other 3 are “not six”:

13. A range of outcomes
With 20 coins, if we get 1 heads, there must be 19 tails:
A cumulative probability is for a range of outcomes: