If an unbiased die marked with -2,-1,0,1,2,3 is thrown five times, the probability that th…

Question

If an unbiased die marked with $-2,-1,0,1,2,3$ is thrown five times, the probability that the product of outcomes is positive, is:

Accepted Answer

$P(\text{positive face})=\dfrac36=\dfrac12$, $P(\text{negative face})=\dfrac26=\dfrac13$ (zero gives product 0, excluded). Product positive: all 5 positive, or exactly 2 negative \& 3 positive, or exactly 4 negative \& 1 positive.

$$P = {}^5C_5\left(\frac12\right)^5+{}^5C_2\left(\frac13\right)^2\left(\frac12\right)^3+{}^5C_4\left(\frac13\right)^4\left(\frac12\right) = \frac{521}{2592}$$

Solutions · 1