If an unbiased die, marked with -2,-1,0,1,2,3 on its faces, is thrown five times, then the…

Question

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 :

Accepted Answer

$${}^5{C_0} \times {3^5} = 243$$

$${}^5{C_2} \times {2^2} \times {3^3} = 1080$$

$${}^5{C_4} \times {2^4}\,.\,3 = 240$$

$$\therefore$$ required probability

$$ = {{243 + 1080 + 240} \over {6 \times 6 \times 6 \times 6 \times 6}} = {{521} \over {2592}}$$

Solutions · 1