List any two applications of conditional probability. You have 9 families you would like to invite to a wedding. Unfortunately, you can only invite 6 families. How many different sets of invitations could you write?

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The probability that an event A occurs given that event E has already occured written as p(A|E) and read as the conditional probability of A given E is

\(p(\frac{A}{E}) = \frac{p(A∩E)}{p(E)}\) , p(E) > 0

Its two applications are

  1. Diagonosis of medical conditions (Sensitivity | Specificity)
  2. Data analysis and model comparision
  3. In Baye’s theorem and Markob process

Here, given

Total families = 9

Families I can invite = 6

Total set of invitation I could write = p C 6

= \(\frac{9!}{(9-6)! \times 6!}\)

= 84

So, 84 different set of invitations can be writtenby me.

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