How do you use the binomial probability formula to find the probability of #x# successes given the probability #p# of success on a single trial for #n=5, x=2, p=0.25#?

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Answer 1 · 2017-12-02T16:06:16

# 135/512#.

Let #p(x)# denote the reqd. prob. Then,

#p(x)=""_nC_xp^xq^(n-x), x=0,1,2,...,n; &, q=(1-p).#

In our case,

#n=5, x=2, p=0.25," & so, "q=1-0.25=0.75#.

#:. p(2)=""_5C_2(0.25)^2(0.75)^(5-2),#

#=(5xx4)/(1xx2)(1/4)^2(3/4)^3,#

#=10*1/16*27/64,#

#=(5xx27)/(8xx64),#

# p(2)=135/512#.