1. Tardigrade
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  4. A robot is at zero position on a straight number line. Each second, it randomly moves either one unit in the positive direction or one unit in the negative direction, the probability being 0.6 in positive direction. The probability that at the end of 5 seconds the robot is 1 unit away from its initial zero position, is

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Q. A robot is at zero position on a straight number line. Each second, it randomly moves either one unit in the positive direction or one unit in the negative direction, the probability being 0.6 in positive direction. The probability that at the end of 5 seconds the robot is 1 unit away from its initial zero position, is

Probability - Part 2

Solution:

$n =5 ; p =\frac{3}{5} ; q =\frac{2}{5}$ $r =2$ or 3
$P (2 \text { or } 3)= P (2)+ P (3)={ }^5 C _2\left(\frac{3}{5}\right)^2 \cdot\left(\frac{2}{5}\right)^3+{ }^5 C _3 \cdot\left(\frac{3}{5}\right)^3 \cdot\left(\frac{2}{5}\right)^2 $
$=10 \cdot\left(\frac{3}{5}\right)^2 \cdot\left(\frac{2}{5}\right)^2\left[\frac{2}{5}+\frac{3}{5}\right]=10 \cdot \frac{9}{25}\left(\frac{4}{25}\right)=\frac{72}{125} \cdot $