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

Question

TestHub · Accepted Answer

The unbiased die is thrown five times such that the product of the outcomes is positive, then either all outcomes are positive or any two are negative.

Either all outcomes are positive or any two are negative.

Now,

$p = p$ (positive) $= \frac{3}{6} = \frac{1}{2}$

$q = p$ (negative) $= \frac{2}{6} = \frac{1}{3}$

Required probability

$= {}^{5}C_{5} {(\frac{1}{2})}^{5} + {}^{5}C_{2} {(\frac{1}{3})}^{2} {(\frac{1}{2})}^{3} + {}^{5}C_{4} {(\frac{1}{3})}^{4} {(\frac{1}{2})}^{1}$

$= \frac{521}{2592}$

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