NCERT Solutions
Class 11 Maths
Probability

Ex.16.3 Q.1
Which of the following cannot be valid assignment of probabilities for outcomes of sample space S = {w1, w2, w3, w4, w5, w6, w7}?
(a)
Here, each of the number p(w) is positive and less than 1.
Sum of probabilities = p(w1) + p(w2) + p(w3) + p(w4) + p(w5) + p(w6) + p(w7)
= 0.1 + 0.01 + 0.05 + 0.03 + 0.01 + 0.2 + 0.6
= 1
Thus, the assignment is valid.
(b) Here, each of the number p(w) is positive and less than 1.
Sum of probabilities = p(w1) + p(w2) + p(w3) + p(w4) + p(w5) + p(w6) + p(w7)
= +
+
+
+
+
+
=
= 1
Thus, the assignment is valid.
(c)
Here, each of the number p(w) is positive and less than 1.
Sum of probabilities = p(w1) + p(w2) + p(w3) + p(w4) + p(w5) + p(w6) + p(w7)
= 0.1 + 0.2 + 0.3 + 0.4 + 0.5 + 0.6 + 0.7
= 2.8 ≠ 1
Thus, the assignment is not valid.
(d)
Here, p(w1) and p(w5) are negative.
Hence, the assignment is not valid.
(e)
Here, p(w7) = > 1
Hence, the assignment is not valid.