Two choices: A and B. P ( A ) = 0.25; P ( B ) = 0.75There are no conditional probabilities or anything. Each choice is independent of the last.

Question

Two choices:   A and   B.  P  (  A  )  =  0.25;   P  (  B  )  =  0.75There are no conditional probabilities or anything. Each choice is independent of the last.

Jovan Wong · Accepted Answer

You want to pick   A twice and   B eight times, so the probability of doing this in a certain order is   P  (  A      )    2    P  (  B      )    8  . But for you, the order doesn&#039;t matter, so you have to divide by the number of ways to choose two things from 10. This is                 (              10      2                  )        =            10      !              8      !      2      !        =  45. So all in all you get             (      45      )              3        8                    4          10      , which you can calculate yourself.In general the formula for (                (              n      r                  )        =            n      !              (      n      −      r      )      !      r      !      , where the exclamation point means &quot;factorial,&quot;   n  !  =  n  ×  (  n  −  1  )  ×  ⋯  ×  2  ×  1. Since n! represents the number of arrangements of   n things, you can interpret this formula as giving you the number of arrangements of your   n things, and then cancelling out the ways you can arrange the   r things you want, and the   n  −  r things you don&#039;t want.

gvaldytist · Accepted Answer

You want the binomial distribution with   p  =  0.25 and   n  =  10 and   k  =  2.he probability of getting exactly   k successes in   n trials [when each trial has success probability   p] is given by                (              n      k                  )            p    k    (  1  −  p      )          n      −      k        .  &quot;

Two choices: A and B . P ( A ) = 0.25 ; P ( B ) = 0.7

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