# Question

A manufacturer of laundry detergent has introduced a new product that it claims to be more environmentally sound. An extensive survey gives the percentages shown in the table.

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

b. Given that a randomly chosen consumer has seen the product advertised, estimate the probability that the person has tried the product.

c. 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. Express the probabilities found in part a and b in terms of A and B.

d. Are A and B independent? Justify your answer.

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

b. Given that a randomly chosen consumer has seen the product advertised, estimate the probability that the person has tried the product.

c. 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. Express the probabilities found in part a and b in terms of A and B.

d. Are A and B independent? Justify your answer.

## Answer to relevant Questions

A board game requires players to roll a pair of balanced dice for each player’s turn. Denote the outcomes by (die 1, die 2), such as (5, 3) for a 5 on die 1 and a 3 on die 2. a. List the sample space of the 36 possible ...A roulette wheel in Monte Carlo has 18 even-numbered slots, 18 odd-numbered slots, a slot numbered zero, and a double zero slot. On August 18, 1913, it came up even 26 times in a row. 10 As more and more evens occurred, the ...A study of the PSA blood test for diagnosing prostate cancer in men (by R. M. Hoffman et al., BMC Family Practice, vol. 3, p. 19, 2002) used a sample of 2620 men who were 40 years and older. When a positive diagnostic test ...a. State in a table the probability distribution for the outcome of rolling a balanced die. (This is called the uniform distribution on the integers 1, 2,., 6.) b. Two balanced dice are rolled. Show that the probability ...For a normal distribution, a. Find the z -score for which a total probability of 0.02 falls more than z standard deviations (in either direction) from the mean, that is, below μ - zσ or above μ + zσ. b. For this z, ...Post your question

0