Probability 1 Question 12
20. The probability that $x _1, x _2$ and $x _3$ are in an arithmetic progression, is
(a) $\frac{9}{105}$
(b) $\frac{10}{105}$
(c) $\frac{11}{105}$
(d) $\frac{7}{105}$
Fill in the Blanks
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Answer:
Correct Answer: 20. (c)
Solution:
- Since, $x _1, x _2, x _3$ are in AP.
$\therefore \quad x _1+x _3=2 x _2$
So, $x _1+x _3$ should be even number.
Either both $x _1$ and $x _3$ are odd or both are even.
$\therefore$ Required probability $=\frac{{ }^{2} C _1 \times{ }^{4} C _1+{ }^{1} C _1 \times{ }^{3} C _1}{{ }^{3} C _1 \times{ }^{5} C _1 \times{ }^{7} C _1}$
$$ =\frac{11}{105} $$
