Advanced Math Topics 5.3 Conditional Probability.

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Presentation transcript:

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 | B) = p(A and 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 & green) = p(blue) xp(green | blue) p(blue & green) = 2/6 x2/5 = 4/30 = 2/15 p(blue & green) = p(blue) xp(green | blue) Rearrange this formula to isolate p(green I blue): p(blue) p(blue & green) = p(green | blue) p(blue & green) p(green | blue) = The conclusion… p(A & B) p(B) p(A | B) =

From the HW P ) 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(B) p(A | B) = p(female & insur.) p(insur.) p(female | insurance) = p(female | insurance) = 44.44% p(female | insurance) =

From the HW P ) It was found that that 22% of females between the age of 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(B) p(A | B) = p(spa & jog) p(jog) p(spa | jog) = p(spa | jog) = 54.55% p(spa | jog) =

From the HW P ) On the board together.

HW P. 256 #2-11