A special die with numbers $1, - 1, 2, - 2, 0$ and $3$ is thrown thrice.
The probability that the total is zero is $\frac{5 k}{216}$ .Find the value of $k$ ?

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Solution

$n (S) = 6.6.6 = 216$
To get sum zero die can have numbers
$- 2, 2, 0 \to 6$ ways
$- 1, 1, 0 \to 6$ ways
$3, - 2, - 1 \to 6$ ways
$- 2, 1, 1 \to 3$ ways
$2, - 1, - 1 \to 3$ ways
$0, 0, 0 \to 1$ ways
$∴ n (E) = 25$
Hence required probability $= \frac{25}{216}$
$\Rightarrow k = 5$

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A special die with numbers 1,−1,2,−2,0 and 3 is thrown thrice. The probability that the total is zero is 5k216.Find the value of k?

n(S)=6.6.6=216To get sum zero die can have numbers−2,2,0→6 ways−1,1,0→6 ways3,−2,−1→6ways−2,1,1→3 ways2,−1,−1→3 ways0,0,0→1 ways∴n(E)=25Hence required probability =25216⇒k=5

A special die with numbers $1, - 1, 2, - 2, 0$ and $3$ is thrown thrice.
The probability that the total is zero is $\frac{5 k}{216}$ .Find the value of $k$ ?

$n (S) = 6.6.6 = 216$
To get sum zero die can have numbers
$- 2, 2, 0 \to 6$ ways
$- 1, 1, 0 \to 6$ ways
$3, - 2, - 1 \to 6$ ways
$- 2, 1, 1 \to 3$ ways
$2, - 1, - 1 \to 3$ ways
$0, 0, 0 \to 1$ ways
$∴ n (E) = 25$
Hence required probability $= \frac{25}{216}$
$\Rightarrow k = 5$