independence and expected value - lehi math -...

Independence and

Expected ValueLESSON 11.4

Objective

• Determine if two events are independent

• Find expected values

Independent vs. Dependent

Independent – an event occurring has no change to future probabilities

Dependent – an event occurring changes future

probability


1.

a. You flip a coin and get ‘heads’. Are you more

likely to get ‘heads’ or ‘tails’ on second flip?

b. Which is more likely when flipping a coin 4 times:

HHHH HTHT


Independence can be determined if

𝑃 𝐴 ∩ 𝐵 = 𝑃 𝐴 ⋅ 𝑃(𝐵)In other words, if the probability of the intersection

(both happening) is the same as the probability of

them happening one after the other, they are

independent.


2. A coin is tossed 3 times.

X: the first toss is heads

Y: the second toss is heads

Z: there are exactly 2 consecutive heads

Are the following events independent?

a. X ∩ Y b. X ∩ Z c. Y ∩ Z

Independence:

𝑃 𝐴 ∩ 𝐵 = 𝑃 𝐴 ⋅ 𝑃(𝐵)


3.

Determine if the events that a customer orders

Landen’s club sandwich and the customer orders

country white bread are independent.


4. Town Cinema is next to Rhiannon’s Bistro. 200

people were surveyed who saw a movie and ate at

the bistro. 80% liked the movie while 60% liked both

the movie and the meal. Assuming independence,

what is that probability that a randomly chosen

moviegoer will like a meal at the bistro?

Conditional Independence

CONDITIONAL PROBABILITY

If 𝑃 𝐵 𝐴 = 𝑃(𝐵), then A did not change the

probability of B, making A and B independent.


5. Hamid rolls a 6-sided die 3 times.

A: the first roll is an odd number

B: there are exactly 2 consecutive odd numbers

Are A and B independent events? Show using

conditional probability.


6. TEN: student is in 10th grade

TWELVE: student is in 12th grade

FT: student prefers field trip

TS: student prefers talent show

Find P(TEN|FT) and P(TEN). Now find P(FT|TEN) and P(FT).


7. M: student selects milk

B: student selects burger

Are events M and B independent?

Expected Value

Using probability, we can find an EXPECTED VALUE.

EX: 200 people sign up for an event but only 80% are

expected to show up. The event staff should plan

for 200 × 80% → 200 × .80 = 160 people to show up.

Expected Value

8. A two-year warranty on a bike covers the bike frame and

the gear shifter, fixing either for free. Without a warranty, fixing

a frame is $225 and a gear shifter is $110.

Madelyne buys a bike. Over a two year period,

P(frame breaking)=0.15 and P(gear shifter breaking)=0.30.

The warranty is $75. Should Madelyne buy the warranty?

Homework

Worksheet 11.4

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