Exercise 2 Page 700

The probability that an event will occur, given that another event has already occurred, is called a conditional probability. There are 52 cards in a standard deck of cards. There are 4 different colored suits - red heart, red diamond, black club, and black spade. Each suit includes an Ace, a King, a Queen, a Jack and numerals from 1 to 10.

Since we want to know the conditional probability of selecting a card number 4 from the deck. Given that the card drawn is black, let's first calculate the number of black cards numbered4.

There is 1 card numbered four in each suit and there are 2 black suits, therefore there are 2 black cards numbered four. Now, we can calculate total number of black cards. black clubcards:& 52/4= 13& [1em] black spadecards:& 52/4= 13& [1em] blackcards:& 13+ 13= 26& The condition that the card selected is black limits the total outcome to 26 cards. Out of those 26 black cards, there are 2 numbered four.

P(4| Black)=Card number four/Black card

SubstituteValues

Substitute values

P(4| Black)=2/26

ReduceFrac

a/b=.a /2./.b /2.

P(4| Black)=1/13

▼

Convert to percent

CalcQuot

Calculate quotient

P(4| Black)=0.076923...

RoundDec

Round to 3 decimal place(s)

P(4| Black)≈0.077

WritePercent

Convert to percent

P(4| Black)≈ 7.7 %

The probability of selecting a black diamond card is 113, which can be also written as 7.7 %.