Question

1. A card is drawn from a deck of 52 cards

What is the P(Red picture card or no ace)?

Show the probability and contingency diagram. Remember that the word OR is the union and you need to use the formula for the union.

2. Of the cars on a used lot, 60% have air conditioning (AC) and 30% have a CD player (CD). 15% of the cars have both. Assume 100 cars on the lot.

A. What is the probability that a car has a CD player, given that it has AC?

B. What is the probability that a car does not have AC, given that it does not have a CD player?

(HINT: Use the Conditional probability formula to calculate the answers)

Answer 1

Here we want to find   P(Red picture card or no ace) = P(Red picture card ) + P( no ace) - P(Red picture card and no ace)

= (26/52) + ( 48/52) - (24/52) = (26 + 48 - 24)/52 = 50/52 = 25/26 = 0.961538

The contingency diagram is as follows:

Red cars Black card Total 1 2 Ace 3 No Ace 4 Total 5 4 48 52 24 26 24 26

2. From the given information, we have.

P( AC ) = 0.60 ; P( CD ) = 0.30 ; P( AC and CD ) = 0.15

A) Here we want to find the probability that a car has a CD player, given that it has AC

Mathematically, P(CD|AC) = P(CD and AC ) / P(AC) = 0.15/0.60 = 1/4 = 0.25

B) Here we want to find the probability that a car does not have AC, given that it does not have a CD player.

Mathematically, P(AC' )/P(CD') = P(AC' and CD') / P( CD') =

So final answer of this part is 0.625