Exercise 39 Page 931

The event of drawing the first king affects the probability of drawing the second one. This is because there is one fewer card from which to choose, and one fewer king to draw. Therefore, the events are dependent.

A standard deck has 52 cards, four of which are kings. P(A)&=4/52 l←Number of kings ←Number of cards P(B|A) is the probability of drawing a king, given that the first card drawn is a king. Since we have already drawn a king, there are 51 cards, from which three of them are kings. P(B|A)&= 3/51 l←Remainingkings ←Remainingcards Finally, according to the formula, to calculate P(AandB) we have to multiply P(A) and P(B|A).

P(AandB)=P(A)* P(B|A)

SubstituteII

P(A)= 4/52, P(B|A)= 3/51

P(AandB)= 4/52* 3/51

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Simplify right-hand side

ReduceFrac

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

P(AandB)=1/13*3/51

ReduceFrac

a/b=.a /3./.b /3.

P(AandB)=1/13*1/17

MultFrac

Multiply fractions

P(AandB)=1/221

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Convert to percent

CalcQuot

Calculate quotient

P(AandB)=0.004525...

RoundDec

Round to 3 decimal place(s)

P(AandB)≈0.005

WritePercent

Convert to percent

P(AandB)≈0.5 %

Probability of the given event is equal to 1221 or about 0.5 %.