A fair die is tossed repeatedly until a $4$ or $6$ is obtained. If $x$ denotes the number of tosses required, then probability that $x \geq 3$ is $\frac{a}{b}$ , where $a$ and $b$ are co-prime, then the value of $| a - b |$ is

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Solution

$P (E) = 1 - P (1) - P (2)$
$= 1 - \frac{2}{6} - \frac{4}{6} \times \frac{2}{6} = \frac{4}{9}$

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A fair die is tossed repeatedly until a 4 or 6 is obtained. If x denotes the number of tosses required, then probability that x≥3 is ab, where a and b are co-prime, then the value of |a−b| is

P(E)=1−P(1)−P(2) =1−26−46×26=49

A fair die is tossed repeatedly until a $4$ or $6$ is obtained. If $x$ denotes the number of tosses required, then probability that $x \geq 3$ is $\frac{a}{b}$ , where $a$ and $b$ are co-prime, then the value of $| a - b |$ is

$P (E) = 1 - P (1) - P (2)$
$= 1 - \frac{2}{6} - \frac{4}{6} \times \frac{2}{6} = \frac{4}{9}$