Which of the following cannot be valid ...

NCERT Class XI Mathematics - Probability - Solutions

Question : 24 of 54

Marks: +1, -0

Which of the following cannot be valid assignment of probabilities for outcomes of sample space S = {

\omega_1, \omega_2, \omega_3, \omega_4, \omega_5, \omega_6, \omega_7

}

Assignment	$\omega_1$	$\omega_2$	$\omega_3$	$\omega_4$	$\omega_5$	$\omega_6$	$\omega_7$
(a)	0.1	0.01	0.05	0.03	0.01	0.2	0.6
(b)	1/7	1/7	1/7	1/7	1/7	1/7	1/7
(c)	0.1	0.2	0.3	0.4	0.5	0.6	0.7
(d)	- 0.1	0.2	0.3	0.4	- 0.2	0.1	0.3
(e)	1/14	2/14	3/14	4/14	5/14	6/14	15/14

Solution:

(a) Sum of probabilities

= 0.1 + 0.01 + 0.05 + 0.03 + 0.01 + 0.2 + 0.6 = 1.00

∴ Assignment of probabilities is valid.

(b) Sum of probabilities

\frac{1}{7}+\frac{1}{7}+\frac{1}{7}+\frac{1}{7}+\frac{1}{7}+\frac{1}{7}+\frac{1}{7}

\frac{7}{7}

= 1

∴ Assignment of probabilities is valid.

= 0.1 + 0.2 + 0.3 + 0.4 + 0.5 + 0.6 + 0.7 = 2.8

Sum of probabilities is greater than 1.

∴ This assignment of probabilities is not valid.

(d) Probability of any event cannot be negative. Therefore, this assignment of probabilities is not valid.

(e) The last probability

\frac{15}{14}

is greater than 1.

∴ This assignment of probabilities is not valid.

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