Cards

Probability Level 1

Caroline has three white cards numbered 1 to 3 and three black cards, also numbered 1 to 3. She chose, at random, one white card and one black card. What is the probability that the sum of the numbers of the cards chosen to be an even number?

3 4 \frac {3}{4} 5 9 \frac {5}{9} 2 3 \frac {2}{3} 1 2 \frac {1}{2}

Victor Paes Plinio by Victor Paes Plinio , 21, Brazil

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3 solutions

Charity Aghahowa
Jun 29, 2014

I wrote out all possible combinations: 9 of them

1 + 1

1 +2

1 + 3

2 + 1

2 + 2

2 + 3

3 + 1

3 + 2

3 + 3

Then only 5 of these 9 were even. Giving you the answer of 5/9 !!!

1 Helpful 0 Interesting 0 Brilliant 0 Confused
Nafi Us-Sabbir
May 1, 2014

suppose, P = the probability that the sum of the numbers of the cards chosen to be an even number.

we know,summation of two numbers is even in two cases. case 1- odd number + odd number; case 2-even number + even number;

consider P1= case 1, P2= case 2; so, P = P1 U P2, here 'U' means the union of two sets P1 And P2.

P1 = (2/3) * (2/3); P2 = (1/3) *(1/3);

so, P = P1 + P2; or,P= 4/9 + 1/9 ; or, P =5/9;

answer : 5/9

1 Helpful 0 Interesting 0 Brilliant 0 Confused
Nida E Falak
Apr 4, 2014

the no. of outcomes are: (black,white)- 1,1 1,2 1,3 2,1 2,2 2,3 3,1 3,2 3,3 we have 9 possible outcomes and 5 outcomes favorable Therefore 5/9

1 Helpful 0 Interesting 0 Brilliant 0 Confused

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