In one jar, I have two balls labelled 1 and 2 respectively. In a second jar, I have three balls labelled 0, 1 and 2 respectively. I draw one ball from each jar, multiply the numbers on the two balls together, and then calculate three to the power of that product, e.g. if I draw 1 and 2, I calculate 3^2=9. Let’s call this number X. What is the probability that the number 1,024 is an exact multiple of X?
Answers
Given : In one jar, two balls labelled 1 and 2 respectively. In a second jar, three balls labelled 0, 1 and 2 . draw one ball from each jar, multiply the numbers on the two balls together, and then calculate three to the power of that product = X
To find : probability that the number 1,024 is an exact multiple of X?
Solution:
A = { 1 , 2 }
B = { 0 , 1 , 2 }
Possible out comes = { (1 , 0) , ( 1, 1) , ( 1, 2) , (2 , 0) , (2 , 1) , ( 2, 2) } = 6
1 * 0 = 0
1 * 1 = 1
1 * 2 = 2
2 * 0 = 0
2 * 1 = 2
2 * 2 = 4
= { 0 , 0 , 1 , 2 , 2 , 4 }
X = 3⁰ , 3⁰ , 3¹ , 3² , 3² , 3⁴
X = { 1 , 1 , 3 , 9 , 9 , 81}
1024 = 2¹⁰ * 1
1024 is only multiple of 1
probability that the number 1,024 is an exact multiple of X = 2/6
= 1/3
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