Question

1. a local bakery sells the freshest bread in town. in fact, 65% of customers who come into this store buy bread. what is the probability that at least 3 customers out of the first 6 will buy bread? 88.3% 23.5% 76.5% 11.7%

Explanation:

Step1: Define binomial parameters

$n=6$, $p=0.65$, $P(X\geq3)=1-P(X<3)=1-[P(X=0)+P(X=1)+P(X=2)]$
Binomial formula: $P(X=k)=\binom{n}{k}p^k(1-p)^{n-k}$

Step2: Calculate $P(X=0)$

$\binom{6}{0}(0.65)^0(0.35)^6=1\times1\times0.001838=0.001838$

Step3: Calculate $P(X=1)$

$\binom{6}{1}(0.65)^1(0.35)^5=6\times0.65\times0.005252=0.02059$

Step4: Calculate $P(X=2)$

$\binom{6}{2}(0.65)^2(0.35)^4=15\times0.4225\times0.01501=0.09510$

Step5: Sum lower probabilities

$P(X<3)=0.001838+0.02059+0.09510=0.1175$

Step6: Compute target probability

$P(X\geq3)=1-0.1175=0.8825\approx88.3\%$

Answer:

88.3%