Question

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?

Answer 1

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:

$P(x\ge 1)=1-P(x=0)=1-0.8^5=0.6723$