Is the product even?

Probability Level 3

You have ten 12-sided fair dice each of which has 1 1 through 12 12 written on its faces. You roll them and take the product of the numbers facing up. If the probability of the product being even can be written as A B \frac{A}{B} , where A A and B B are coprime positive integers. What is the value of A + B A+B ?

2 3 5 513 1023 1025 2047 2049

Saad Khondoker by Saad Khondoker , 21, Bangladesh

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1 solution

Saad Khondoker
Mar 9, 2021

For the product to be odd, all the numbers facing up should be odd.

The probability of getting odd face up of a dice is 6 / 12 = 1 / 2 6/12=1/2

All the dice are independent. So, the probability of getting all of them odd is = ( 1 / 2 ) 10 = (1/2)^{10}

So, the probability of the product to be even = 1 − ( 1 / 2 ) 10 = 1023 / 1024 = 1-(1/2)^{10}=1023/1024

So, A + B = 1023 + 1024 = 2047 A+B=1023+1024=2047

2 Helpful 0 Interesting 1 Brilliant 0 Confused

Then why is the correct option 1025?

Jason Gomez - 3 months ago

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