A fair die is rolled four times. If the probability that outcome of each of the roll is at least as large as the outcomes of the preceding roll, can be expressed as \frac{a}{bc}, where a, is natural number & bc is two digit numbers, then

Engineering

Mathematics

Conditional Probability

Question

A fair die is rolled four times. If the probability that outcome of each of the roll is at least as large as the outcomes of the preceding roll, can be expressed as $\frac{a}{bc}$ , where a, is natural number & bc is two digit numbers, then

a = b

3c – a $\div$ b = 4

a + b + c = 15

c + a $\div$ b = 3

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$N_{1} \leq N_{2} \leq N_{3} \leq N_{4}$

$\frac{^{6} C_{4} +^{6} C_{3} \times^{3} C_{1} +^{6} C_{2} \times 3 +^{6} C_{1}}{6 \times 6 \times 6 \times 6} = \frac{7}{12} .$