Problem

21 14) A 6 -sided die is, with sides numbered $1-6$, is biased so that the probability of rolling a 5 is $x$, where $x>0$ a) If the die is rolled twice, find, in terms of $x$, the probability of rolling a 5 only in the first roll

Solution

Step 1 :Let the probability of rolling a 5 be x, and the probability of not rolling a 5 be (1 - x).

Step 2 :To find the probability of rolling a 5 only in the first roll, we need to consider the probability of rolling a 5 in the first roll and not rolling a 5 in the second roll.

Step 3 :The probability of rolling a 5 only in the first roll, in terms of x, is x*(1 - x).

Step 4 :\(\boxed{x(1-x)}\)

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