Quantitative Methods for Business Please explain, thank you P(s) P(s) + P(s2) + ... + P(sN)...

Question

Question

Quantitative Methods for Business

P(s) P(s) + P(s2) + ... + P(sN) = 1 1

Please explain, thank you

math Statistics-And-Probability

Answer 1

Answer #1

The above formula os nothing but shows that sum of probability of all independent events in a sample space S is equal to 1.

Example: Suppose you toss 3 coins and note the output. The output of one coin doesn't impact other. The sample space becomes:

S = {HHH, TTT, HHT, HTH, THH, TTH, THT, HTT}

Now if you see, the probability of occurence of each event is equal to 1/8.

Hence,

P(S) = 1/8 + 1/8 +1/8 + 1/8 + 1/8 + 1/8 + 1/8 + 1/8 = 1

So, if a sample space consists of 'n' independent events s1,s2,s3...sn with probabilities P(s1), P(s2), P(s3)...P(sn)

the sum of probabilities is always equal to 1

so, P(s1) + P(s2) + P(s3) + ... + P(sn) = 1

Answer 2

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