SATHEE: Probability 1 Question 12

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) $\frac{10}{105}$

(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.

$∴ x_{1} + x_{3} = 2 x_{2}$

So, $x_{1} + x_{3}$ should be even number.

Either both $x_{1}$ and $x_{3}$ are odd or both are even.

$∴$ Required probability $= \frac{^{2} C_{1} \times^{4} C_{1} +^{1} C_{1} \times^{3} C_{1}}{^{3} C_{1} \times^{5} C_{1} \times^{7} C_{1}}$

$= \frac{11}{105}$

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Probability 1 Question 12

20. The probability that x1,x2 and x3 are in an arithmetic progression, is

Fill in the Blanks

Answer:

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20. The probability that $x_{1}, x_{2}$ and $x_{3}$ are in an arithmetic progression, is