3-3 Multiple Events 21 October 2010 While Im gone Groups of three - - PDF document

3-3 Multiple Events 21 October 2010

While I’m gone

• Groups of three

– Two players, one counter

• Play rock-paper-scissors
• Best of three wins throws wins game
• Count keeps track of who threw what, (including

names) and who won each game

• Keep playing until I return, switch off roles, if you’d

like Independent Events

• Several events happening, simultaneously or consecutively.
• Independent events

– The outcome of an event does not depend on the previous event, nor does it have an effect on the next event – For example, rolling dice, flipping a coin, or picking a card from a deck and replacing same before drawing the next

• Dependent events

– An event changes the sample space for the next event. – For example, drawing a card and keeping it before the next card. – The probabilities might have to be recalculated for the next event

Finding Probability of multiple events

• If events A and B are independent, the probability of

both events occurring is the product of the individual

• probabilities. In other words:

– P(A and B) = P(A) · P(B)

• The probability of flipping heads twice in a row:

– P(Heads) = – P(Heads and Heads) =

• The probability of rolling two consecutive ‘sevens’

– P(7) = – P(7 and 7) =

3-3 Multiple Events 21 October 2010

Independent events

• The probability of having three daughters

– P(1 daughter) = – P(Three daughters) =

• Acing a multiple choice quiz of five questions each

with five choices by guessing?

– P(1 correct) = – P(Five correct) =

More probability

• Making consecutive 3-point attempts
• 10 consecutive free throws
• Three different baskets in a row

4 10 3 pointer Free throw Field Goal Missed 8 32 Made 20 36

Dependent events

• We have jar of 16 coins, 4

each of quarters, nickels, dimes, and pennies. What is the probability of picking two consecutive pennies if we don’t replace the first?

• P(First penny) =
• However, once we pick the

first penny, the contents of the jar has changed, therefore:

• P(Second penny) =
• Finally, the probability of

picking two consecutive pennies is

• P(Two pennies) =

3-3 Multiple Events 21 October 2010

Probability of Multiple (Consecutive) Events Live example

• 1. Three consecutive red

circles with replacement

• 2. Three consecutive red

circles without replacement

• 3. A blue triangle, red

circle, blue circle, red triangle without replacement

• 1. Two shapes that are

either red or circles w/o replacement

• 2. A blue shape followed

by a red shape with replacement

• 3. Two triangles w/o

replacement Dependent events

• Picking two sticks of gum w/o replacement
• Picking three peppermints w/o replacement
• Picking two lifesavers or spearmint candies

Peppermint Spearmint Wintergreen Gum 10 15 11 Lifesaver 12 8 4

3-3 Multiple Events 21 October 2010

More live examples

• 1. What is the probability of drawing

two aces from a deck of cards… – If the first ace is replaced – If the first ace isn’t replaced?

• 2. What is the probability of drawing a

hand of five hearts?

• 3. What is the probability of drawing a

five-hand flush (same suit)?

• 4. P(Two Jacks with replacement) =
• 5. P(Three of a kind w/o) =
• 6. P(five red cards w/o replacement) =

Probability

• The probability of purchasing a defective widget is

2%. If I buy 3 widgets what is the probability that

• 1. All three are defective?
• 2. All three are OK
• 3. At least one is defective

More probability

• Punxsutawney Phil has predicted 13 early springs

and 99 late winters.

• P(Early Spring) =
• P(Two consecutive early springs) =
• Find the probability of at least one early spring in

the next four years

3-3 Multiple Events 21 October 2010

• I need to pick a committee of three students from

my engineering class. There are seven frosh, five sophomores, three juniors, and 10 seniors. Find the following probabilities

• 1. All three juniors make up the committee
• 2. The committee includes a junior, senior, and

sophomore