# Probability How likely it is that something will happen.

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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 = - PowerPoint PPT Presentation

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• Probability

How likely it is that something will happen.

• p: symbol to represent the probability of a particular outcome.

• # of ways an event can occurp = 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 11 2 2 2 3 2 4 2 5 2 6 21 3 2 3 3 3 4 3 5 3 6 31 4 2 4 3 4 4 4 5 4 6 41 5 2 5 3 5 4 5 5 5 6 51 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 cards13 hearts3 cards that are face cards and hearts

• Prob A + Prob B - (Prob AB)

12 13 3 52 52 52