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  • If an unbiased die, marked with  on its faces, is thrown five times, then the proba

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 :

Option: 1

\frac{881}{2592}


Option: 2

\frac{27}{288}


Option: 3

\frac{440}{2592}


Option: 4

\frac{521}{2592}


Answers (1)

best_answer

Unbiased die. Marked with -2, -1, 0, 1, 2, 3

Product of outcomes is positive if

All time get positive number, 3 time positive and 2 time negative, 1 time positive and 4

time negative. P (Product of the outcomes is positive)

=\underbrace{{ }^5 \mathrm{C}_5\left(\frac{3}{6}\right)^5}_{\text {All positive }}+\underbrace{{ }^5 \mathrm{C}_3\left(\frac{3}{6}\right)^3\left(\frac{2}{6}\right)^2}_{\text {3positive, 2negative }}+\underbrace{{ }^5 C_1\left(\frac{3}{6}\right)\left(\frac{2}{6}\right)^4}_{\text {1positive, 4negative }}

\begin{aligned} & =\frac{3^5}{6^5}+\frac{10 \times 3^3 \times 2^2}{6^5}+\frac{5 \times 3 \times 2^4}{6^5} \\ & =\frac{1563}{6^5}=\frac{521}{2592} \end{aligned}

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