Miscellaneous Question 29
- Four dice are thrown simultaneously.
I. Probability that all the four dice show even digits.
II. Probability that all the four dice show different digits.
(1) I $<$ II
(2) I $>$ II
(3) $I=I$
(4) I $\geq$ II
(5) No relation
Show Answer
Correct Answer: 29. (1)
Solution:
- (1) Total number of elements in the sample space
$=6 \times 6 \times 6 \times 6=(6)^{4}$
I. Number of even digits on a dice $=3$
Number of favourable events $n$ $\left(\mathrm{E}_{\mathrm{T}}\right)=(3)^{4}$
II. Number of favourable events $n$ $\left(\mathrm{E}_{\text {II }}\right)=6 \times 5 \times 4 \times 3=360$
$\therefore \quad p\left(\mathrm{E}_{\mathrm{I}}\right)=\frac{(3)^{4}}{(6)^{4}}=\frac{1}{16}$
$p\left(\mathrm{E}_{\mathrm{II}}\right)=\frac{360}{(6)^{4}}=\frac{5}{18}$
$\frac{5}{18}>\frac{1}{16}$
$\therefore \quad$ I $<$ II
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