Conditional Probability

Conditional Probability

The probability of an event A, given the occurrence of some other event B:

Ex: A card is selected from a standard 52 card deck. If a red card is selected, what is the probability it is a King?

2522652

113

and P A B

P A BP B

king and red

red

P

P

Given (B)

Desired (A)

Want: king redP

Example 1

On the midway at the county fair, there are many popular games to play. One of them is “Flip to Spin or Roll.” You start by flipping a coin. If heads comes up, you get to spin the big wheel, which has ten equal sectors: three red, three blue, and four yellow. If the coin shows tails, you get to roll a cube with three red sides, two yellow sides, and one blue side. If your spin lands on blue, or if the blue side of the cube comes up, you win a stuffed animal.

Suppose that you know that Tyler won a stuffed animal. Figure out what the probability that he started off with heads.

Example 1: Area Model

310

HR HB HY

TR TB TY

25

310

12

12

320

15

320

14

16

112

R B Y

H

T

CO

IN

Wheel

CubeR B Y1

213

16

heads given that he wonP

320

730

Heads and Blue

Win

P

P 9

14 64.3%

If you make an area diagram, it is ok to scale the lengths differently.

WinP

Heads and BlueP

Find the probabilities.

320

3 120 12

Example 2A survey of 500 adults asked about college expenses. The

survey asked questions about whether or not the person had a child in college and about the cost of attending college. Results are shown in the table below:

Cost too Much Cost Just Right Cost Too Low

Child in College 0.30 0.13 0.01

Child not in College 0.20 0.25 0.11

Suppose one person is chosen at random. Given that the person has a child in college, what is the probability that he or she ranks the cost of attending college as “cost too much”?

0.30 0.300.44 0.682

"child in college "an"cost to

"child

o muc

in co

d

l "

h"

lege

P

P

Givenchild in college

Desiredcost too

much

Child in College

Cost too Much

0.30 0.13 0.01

"cost too much "child in cWant oll: "" egeP