A crooked die and a straight die

Probability Level 3

A crooked six-sided die and a fair six-sided die are rolled at the same time.

The crooked die has the following probabilities $P(n)$ of rolling the number $n$ :

$P(1) = 1/2$
$P(2) = 1/4$
$P(3) = 1/8$
$P(4) = 1/16$
$P(5) = 1/32$
$P(6) = 1/32$

If the probability that they roll the same number is of the form $\dfrac ab$ , where $a$ and $b$ are coprime positive integers, find $a+b$ .

For more Permutations quizzes.

The answer is 7.

1 solution

Geoff Pilling
May 3, 2016

It really doesn't matter what the probabilities are on the crooked die as long as it has a probability $1$ of rolling an interger $1 \leq n \leq 6$ . The fair die has a probability of $1$ in $6$ of matching it, or $1/6$ . So, the answer is $1+6=\boxed7$

A crooked die and a straight die

For more Permutations quizzes.

The answer is 7.

1 solution

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