For the following be sure to give the appropriate probabilit

For the following be sure to give the appropriate probability statements, show work, and give probability values to 4 decimal places where applicable.

a. Estimate the probability that a randomly chosen consumer would have seen advertising for the new product and tried the product.

b. Estimate the probability that at least one of TWO randomly chosen independent consumers would have seen the ad.

c. Given that a randomly chosen consumer has seen the product advertised, estimate the probability that the person has NOT tried the product.

d. Let A be the event that a consumer has tried the product. Let B be the event that a consumer has seen the product advertised. Are A and B independent? Justify your answer with probabilities and explanation.

View comments (2)

Result of Advertising for New Laundry Product Tried the New Product Yes 10% 5% No 25% 60% Advertising Status Have not seen the ad

Solution

A)

From the table,

P(seen and tried) = 0.10 [ANSWER]

*****************

b)

Here,

P(seen) = 0.10 + 0.25 = 0.35

Now,

P(at least one seen) = 1 - P( no one seen) = 1 - (1 -0.35)^2

= 0.5775 [ANSWER]

****************

c)

P(not tried|seen) = P(tried and seen) /P(seeb) = 0.25 / (0.10 + 0.25)

= 0.714285714 [answer]

***************

d)

As in part C,

P(not A|B) = 0.714285714

And

P(not A) = 0.25 + 0.60 = 0.85

As P(not A|B) =/= P(not A), then THEY ARE NOT INDEPENDENT. [ANSWER]

(Somehow, B influenced A, that is.)