A company has been running a television advertisement for one of its new products. A survey was conducted. Based on its results, it was concluded that an individual buys the product with probability 56%, if he/she saw the advertisement, and buys with probability 8%, if he/she did not see it. Twenty-five percent of people saw the advertisement.
a) Plot a tree diagram with probability for the problem above.
b) What is the probability that a randomly selected individual will buy the new product?
c) What is the probability that at least one of randomly selected five individuals will buy the new product?
a)
b)
the probability that a randomly selected individual will buy the new product and he saw the advertisement:
"P_1=0.25\\cdot0.56"
the probability that a randomly selected individual will buy the new product and he did not see the advertisement:
"P_2=0.75\\cdot0.08"
the probability that a randomly selected individual will buy the new product :
"P=P_1+P_2=0.25\\cdot0.56+0.75\\cdot0.08=0.2"
c)
for binomial distribution:
"P(x=k)=C^k_np^k(1-p)^{n-k}"
"p=0.2,n=5"
the probability that at least one of randomly selected five individuals will buy the new product:
"P(x\\ge 1)=1-P(x=0)=1-0.8^5=0.6723"
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