24. Which of the following can not be valid assignment of probabilities for outcomes
of sample Space S = {ω1, ω2, ω3, ω4, ω5, ω6, ω7,}
Assignment ω 1 ω 2 ω 3 ω 4 ω 5 ω 6 ω 7
(a) 0.1 0.01 0.05 0.03 0.01 0.2 0.6
(b)
(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)
24. Which of the following can not be valid assignment of probabilities for outcomes
of sample Space S = {ω1, ω2, ω3, ω4, ω5, ω6, ω7,}
Assignment ω 1 ω 2 ω 3 ω 4 ω 5 ω 6 ω 7
(a) 0.1 0.01 0.05 0.03 0.01 0.2 0.6
(b)
(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 Answer
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24. (a) P (S) = P (W1) + P (W2) +P (W3) + P (W4) +P (W5) +P (W6) +P (W7)
P (S) = 0.1 + 0.01 + 0.05 + 0.03 + 0.01 + 0.2 + 0.6
P (S) = 1
As the probability of sample space is ‘one’ the given assignment of probabilities is valid.
(b) P (S) = P (W1) + P (W2) +P (W3) + P (W4) +P (W5) +P (W6) +P (W7)
P (S) =
.
P (S) = 1
Hence, the given assignment of probability is valid.
(c) P (S) = P (W1) + P (W2) +P (W3) + P (W4) +P (W5) +P (W6) +P (W7)
= 0.1 + 0.2 + 0.3 + 0.4 + 0.5 + 0.5 + 0.6 + 0.7
= 2.8
i.e., P (S) > 1
As probability of the sample space S should always be ‘1’. The given assignment is invalid.
(d) Here P (W1) =
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