Let #X# be a binomial random variable with #p=0.6# and #n=10#. What is #P(X > 8) #?

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Answer 1 · 2017-07-01T13:07:28

# P(X>8)=0.0463574016#

Given that, #X# is a Binomial Random Variable, with,

parameters, #p=0.6, and, n=10,# denoted by,

# X~~ B(10,0.6).#

#:. q=1-p=0.4#

Knowing that, for #X~~B(n,p),#

#P(X=x)=""_nC_xp^xq^(n-x), x=0,1,2,...,n.#

Now, the Reqd. Prob.=#P(X>8),#

#=P(X=9)+P(X=10),#

#=""_10C_9(0.6)^9(0.4)^1+""_10C_10(0.6)^10 (0.4)^0,#

#=10(0.6)^9(0.4)+1(0.6)^10(1),#

#=4(0.6)^9+(0.6)^10,#

#=(0.6)^9(4.6),#

# rArr P(X>8)=0.0463574016#