Exercise 116 Page 263

Practice makes perfect

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. To decide the number of favorable outcomes, we must consider how many of the desired card are in the deck. Of the 52 cards, 4 of them are kings and another 4 are queens. With this, we can find the two first probabilities. P(king)=4/52=1/13 [0.8em] P(queen)=4/52=1/13 To find the last probability, we have to consider how many clubs there are in the deck. There are 4 different suits which means 524=13 of them are clubs. With this, we can find the probability of drawing a club. P(club)=13/52=1/4

b 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 4 kings and 13 clubs. Notice that one club is the king of clubs (the union of kings and clubs). With this information, we can calculate the probability of choosing a king or a club.

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

SubstituteValues

Substitute values

P(king or club) = 13/52+4/52-1/52

AddSubFrac

Add and subtract fractions

P(king or club) = 13+4-1/52

AddSubTerms

Add and subtract terms

P(king or club) = 16/52

ReduceFrac

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

P(king or club) = 4/13

Compared to Part A, we see that P(king or club) is greater than any of the probabilities calculated in Part A.

c Like in Part B, to calculate P(king or queen), we have to use the Addition Rule. In this case, there is no overlap between kings and queens. Therefore, the number of favorable outcomes is the sum of the number of kings and queens in the deck

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

SubstituteValues

Substitute values

P(king or queen) = 4/52+4/52-0/52

AddSubFrac

Add and subtract fractions

P(king or queen) = 4+4-0/52

AddSubTerms

Add and subtract terms

P(king or queen) = 8/52

ReduceFrac

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

P(king or queen) = 2/13

We see that P(king or queen) is greater than any of the probabilities calculated in Part A.

d This time, to calculate the probability of not getting a face card, we can subtract the number of face cards from the number of cards in the deck. There are 4 of each face card so the total number of face cards is 4* 3=12. With this, we can determine the number of favorable outcomes. That is, cards that are not face cards.

Favorable outcomes: 52-12=40 Now we can determine the probability of not picking a face card. P(not a face card)=40/52=10/13