Question

The COV-19 virus has virtually changed the way we work, study and shop. People are scared and frightened of contracting the deadly virus. Traditional grocery stores such as Loblaws, Longo’s, etc. have seen fewer shoppers, who also spent less time in the stores. A survey of 500 Canadian grocery shoppers was conducted last week to find out if the scare of contracting the COV-19 virus, (very scared , VS) or (somewhat scared, SS) has affected their grocery shopping habits: whether they purchase groceries online (OL) or they purchase at a conventional grocery store (TS).The survey reported that 400 shoppers purchased online and that 150 of all shoppers were somewhat scared. The survey also reported that 75 Canadians shopped online given that the shopper was somewhat scared.

a) Construct a cross-classification (or contingency) table with joint and marginal probabilities. [or you can construct a tree diagram].

b) What is the probability that a randomly selected shopper is very scared and shops online?   

c) What is the probability that a randomly selected very scared shopper buys from a traditional grocery store?

d) What is the probability that a shopper who shops online is somewhat scared?

e) What is the probability that a randomly selected shopper is somewhat scared or shops online?

f) Are “somewhat scared” and “online” independent events or dependent events or mutually exclusive events? Your answer must include supporting probability calculations.

Answer 1