Exercise 126 Page 204

a To determine probability, we divide the number of favorable outcomes with the number of possible outcomes.

P=Number of favorable outcomes/Number of possible outcomes In a deck of cards there are 52 cards, which means there are 52 possible outcomes. A card less than 5 includes cards that are 1-4 from all 4 suits (we count the aces as 1). This gives a total of 4* 4= 16 cards. With this information we can find the probability of drawing a card that is less than 5. P(less than 5)=16/52=4/13

b The complement of P(less than 5) describes every outcome in P(5 or more). We can calculate this by subtracting the probability of drawing a card less than 5 from 1.

P(5 or more)=1-P(less than 5) From Part A, we know the probability of P(less than 5).

P(5 or more)=1-P(less than 5)

Substitute

P(less than 5)= 4/13

P(5 or more)=1- 4/13

OneToFrac

Rewrite 1 as 13/13

P(5 or more)=13/13-4/13

SubFrac

Subtract fractions

P(5 or more)=9/13

c The probability of the union of two events, A and B, happening can be found using the Addition Rule.

P(A or B) =P(A)+P(B)-P(A and B)In a deck there are two types of red cards. Hearts ♡ andDiamonds ◊ There are 13 hearts and 13 diamonds for a total of 26 red cards. Also, each suit has 3 face cards and therefore we have a total of 3* 4=12 face cards in the deck. However, 6 of these are red cards, which means they are already included in the red cards. This is the intersection of face cards and red cards.

P(A or B) =P(A)+P(B)-P(A and B)

SubstituteValues

Substitute values

P(red or face cards) = 26/52+12/52-6/52

AddSubFrac

Add and subtract fractions

P(red or face cards) = 26+12-6/52

AddSubTerms

Add and subtract terms

P(red or face cards) = 32/52

ReduceFrac

a/b=.a /4./.b /4.