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

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

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

$=120xx0.003375xx0.32057708828125$ .

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