Question

What is the probability that , in a group of 200 random people , at least two of them have the same triple of initials (such as JTK for James Tiberius Kirk)

Answer 1

The probability is P(X >= 2).

200 random people, n = 200

Let us consider the Binomial expression

i.e.,

P(X = r) = nCr*p^r*q^(n-r)

Here we have to assume that the 3 initials are equally likely events.

i.e.,

p = 1/3

q = 1 - 1/3

= 2/3

Required probability = P(X >= 2)

= 1 - [P(X = 0) + P(X = 1)]

= 1 - [200C0*(1/3)^0*(2/3)^200 + 200C1*(1/3)^1*(2/3)^199]

= 1 - [1*1*(2/3)^200 + 200*(1/3)*(2/3)^199]

= 1 - [(2/3)^200 + 200*(1/3)*(2/3)^199]

= 1 - (2/3)^200 - 200*(1/3)*(2/3)^199

Probability is truly how possibly something is to happen. every time we're unsure about the final results of an event, we will talk about the possibilities of certain consequences and how probably they are. The evaluation of events ruled by means of possibility is called records.

3 styles of probability

• Classical
• Relative Frequency Definition.
• Subjective possibility.

Learn more about probability here brainly.com/question/24756209

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