Probability
How likely it is that something will happen.
p: symbol to represent the probability of a particular outcome.
# of ways an event can occur
p =
total # of events
The event: rolling a 3 with one die
1 (# of ways the event occurs)
p =
6 ( total # of possible events)
Event: rolling a 5 with a pair of dice
# of ways the event can occur: 4
1 4
2 3
3 2
4 1
Total # of events : 36
1 1 2 1 3 1 4 1 5 1 6 1
1 2 2 2 3 2 4 2 5 2 6 2
1 3 2 3 3 3 4 3 5 3 6 3
1 4 2 4 3 4 4 4 5 4 6 4
1 5 2 5 3 5 4 5 5 5 6 5
1 6 2 6 3 6 4 6 5 6 6 6
Probability of rolling 5 with a pair of dice
4 (# of ways the event can occur)
p =
36 (total number of events)
1
p= p = .11
9
All events: 50 pieces of paper
10 green
20 red
15 yellow
5 blue
(papers are returned after each draw)
1) Prob. of two events both occurring
Event A and Event B
( Prob. A) (Prob. B)
Event: drawing a red and a yellow
All events: 50 pieces of paper
10 green
20 red
15 yellow
5 blue
(papers are returned after each draw)
Event: drawing a red and a yellow
prob of red and prob of yellow
20 15
50 50
20 15 300 3
50 50 2500 25
or:
2 3 6 3
5 10 50 25
p = .12
Probability does not have memory !
If the event is defined as two draws then this method applies.
If the event is limited to the second draw only, the probability is based on that event alone
2) The probability of either of two mutually exclusive events occurring is the sum of their probabilities.
Prob A or Prob B
(Prob A ) + (Prob B)
Event: in one draw, choosing a yellow or red.
All events: 50 pieces of paper
10 green
20 red
15 yellow
5 blue
(papers are returned after each draw)
Event: in one draw, choosing a yellow or red.
20 15 35 7
50 50 50 10
p = .7
Mutually Exclusive:
When two events can not co-occur.
Events that are not mutually exclusive:
Using a standard deck of 52 playing cards,
Drawing a face card or a heart.
12 faces cards
13 hearts
3 cards that are face cards and hearts
Prob A + Prob B - (Prob AB)
12 13 3
52 52 52
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