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Probability — Maths STD 12 Science — Question

Gujarat 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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