JEE MAIN - Mathematics (2023 - 30th January Morning Shift - No. 10)
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 :
$$\frac{27}{288}$$
$$\frac{521}{2592}$$
$$\frac{440}{2592}$$
$$\frac{881}{2592}$$
Explanation
$${}^5{C_0} \times {3^5} = 243$$
$${}^5{C_2} \times {2^2} \times {3^3} = 1080$$
$${}^5{C_4} \times {2^4}\,.\,3 = 240$$
$$\therefore$$ required probability
$$ = {{243 + 1080 + 240} \over {6 \times 6 \times 6 \times 6 \times 6}} = {{521} \over {2592}}$$
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