Bill and ben each have 3 cards numbered 4,5,6
they each take one of their cards. They add together the two numbers on the cards
a)what is the probability that their answer is an odd number
b) What is their probability that their answer is less than 11
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Answers
Given : Bill and ben each have 3 cards numbered 4,5,6 . they each take one of their cards. They add together the two numbers on the cards
To find : probability that their answer is an odd number , probability that their answer is less than 11
Solution:
Bill and ben each have 3 cards numbered 4,5,6
Bill = { 4 , 5 , 6 }
Ben = { 4 , 5 , 6 }
Each take 1 of their cards
Hence All possible outcomes
= { (4 , 4) , ( 4 , 5) , ( 4 , 6) , ( 5 , 4) ,( 5 , 5) , ( 5 . 6) , ( 6 , 4) , ( 6 ,5 ) , ( 6 , 6) }
Total 9 possible outcomes
in terms of Sum possible out comes are
{ 8 , 9 , 10 , 11 , 12 }
8 = 4 + 4
9 = 4 + 5 , 5 + 4
10 = 4 + 6 , 5 + 5 , 6 + 4
11 = 5 + 6 , 6 + 5
12 = 6 + 6
Sum as odd number = 9 & 11
=> 4 times
Total outcome = 9
Probability that their answer is an odd number = 4/9
probability that their answer is less than 11
= 6/9
= 2/3
probability that their answer is less than 11 = 2/3
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a) The probability that their answer is an odd number is 4/9
b) The probability that their answer is less than 11 is 2/3
Step-by-step explanation:
The people playing are Bill and Ben. The number of the cards are 4, 5 and 6.
The possible outcomes of the cards are:
(4, 4), (4, 5), (4, 6), (5, 4), (5, 5), (5, 6), (6, 4), (6, 5) and (6, 6)
The sum of the outcomes are:
{8, 9, 10, 9, 10, 11, 10, 11, 12}
Thus, there are 9 possible outcomes.
Probability = (Desired outcome)/(Total outcome)
a) Odd number:
Probability of odd number = 4/9
b) Less than 11:
Probability of number less than 11 = 6/9 = 2/3