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Advanced Math Topics

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Advanced Math Topics

5.3 Conditional Probability

Notes

With Conditional Probability, the probability of an event changes on what

has happened in previous events.

p(A | B)

= probability of A given that B has happened

p(A and B)

p(A | B)=

p(B)

We can analyze why this is the formula…

There are 2 green, 2 blue, and 2 red marbles in a bag. You selected 2 marbles

Find p(picking a blue and a green).

p(blue) x

p(green | blue)

p(blue & green) =

Rearrange this formula to isolate

p(green I blue):

2/6 x

2/5

p(blue & green) =

= 4/30

= 2/15

p(blue) x

p(green | blue)

p(blue & green) =

p(blue)

p(blue)

p(blue & green)

= p(green | blue)

p(blue)

p(blue & green)

p(green | blue) =

p(blue)

The conclusion…

p(A & B)

p(A | B) =

p(B)

From the HW P. 256

2) 72% of all hospitalized senior citizen patients have medical insurance. The

records indicate that 32% of all patients are females and have medical

insurance. If a patient is selected at random, what is the probability that the patient

is a female given that the patient has medical insurance?

p(A & B)

p(A | B) =

p(B)

p(female & insur.)

p(female | insurance) =

p(insur.)

.32

p(female | insurance) =

.72

44.44%

p(female | insurance) =

From the HW P. 256

4) It was found that that 22% of females between the age of 20-30 years jog to

stay in shape. 12% of the females jog and exercise at a health spa. If a female

between the age of 20 to 30 years who is jogging is randomly selected, what is

the probability that she exercises at a health spa?

p(A & B)

p(A | B) =

p(B)

p(spa & jog)

p(spa | jog) =

p(jog)

.12

p(spa | jog) =

.22

54.55%

p(spa | jog) =

From the HW P. 256

11) On the board together.

HW

P. 256 #2-11