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Probability — MATHS STD 12 Science — Question

Rajasthan BoardEnglish MediumSTD 12 ScienceMATHSProbability2 Marks
Question
A ordinary cube has four plane faces, one face marked $2$ and another face marked $3,$ find the probability of getting a total of $7$ in $5$ throws.
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Answer

A cube has total $6$ faces.
Total possible outcomes in $5$ throws $= 6 \times 6\times 6 \times 6 \times 6 = (6)^5$
The only way of getting $7$ is by getting two $2s$ and one $3.$
Total possible ways $=\frac{\text{P}^5_3}{2!}$
$=\frac{5\times4\times3\times2\times1}{2\times1\times2\times1}$
$=30$
Now, $P($getting $7$ in $5$ throws$) =\frac{30}{6^5}=\frac{5}{6^4}$

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