A baker blends 600 raisins and 400 chocolate chips into a dough mix and, from this, makes 500 cookies.Find the probability that a randomly chosen cookie will have at least two bits (raisins or chips) in it.?

Number of raisins and chocolate chips in a cookie

n = 600+400 = 1000

Probability that a randomly chosen cookie

\$*p = \frac(1)(500)*\$

Calculation λ

λ = np = \$1000\times\frac(1)(500)\$ = 2

Poisson distribution is written as

X~P(λ) ⇒ X~P(2)

Probability that a randomly chosen cookie will have at least two bits (raisins or chips) is given as.

P(X≥2).

Poisson distribution P(X=x) = \$(e^(-λ) λ^x)/x!\$

P(X≥2).

1 - [P(X=0) + P(X=1)]

P(X≥2).

\$(e^(2) 2^0)/(0!) + (e^(2) 2^1)/(1!)\$

P(X≥2).

\$2.718^(2) + 2.718^(2)×2\$

Probability that a randomly chosen cookie will have at least two bits P(X≥2).

0.5940

Answer

D