A jar of M&Ms contains 100 candy pieces, 15 are red. a handful of 10 is selected. What is the probability that 3 of the 10 selected are red?

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Answer 1 · 2018-02-26T05:24:08

#"Approx. "0.13#.

Let us call success #S=#the event that a red candy is

selected from jar.

In the jar containing #100# candies, there are #15# red candies.

Hence, the Probability of Success, #P(S)=p=15/100=3/20#.

#:. q=1-p=17/20#.

Out of #10# candies selected, let #X=x# denote the no. of success,

i.e., no. of red candies.

Then, #X# is a Binomial Random Variable with parameters

#n=10, p=3/20#. Therefore,

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

In our case, #P(X=x)=p(x)=""_10C_x(3/20)^x(17/20)^(10-x), x=0,1,...,10#.

#:."The Reqd. Prob.="p(3)=""_10C_3(3/20)^3(17/20)^(10-3)#,

#={(10xx9xx8)/(1xx2xx3)}(0.15)^3(0.85)^7#,

#=120xx0.003375xx0.32057708828125#.

#rArr"The Reqd. Prob.="0.12983372075390625~~0.13#.