Question

how would you do this, could someone explain with steps please

For a random person looking for a jolt of caffeine, the probability that they would go to Tim Horton’s over Starbucks is 65%. Those who go to Starbucks will get coffee 80% the time and a specialty drink 20% of the time. Those who go to Tim Horton’s will get the coffee 90% of the time and a specialty drink 10% of the time. What is the probability that a random person going to a coffee shop, either Starbucks or Tim Horton’s,ends up purchasing a coffee?

A. <0.6

B. 0.6-0.7

C. 0.7-0.8

D. 0.8-0.9

E. 0.9-1.0

Answer 1

the probability that a random person going to a coffee shop, either Starbucks or Tim Horton’s,ends up purchasing a coffee
= It means the person doesn't get the speciality drink in both the places

So,
Desired probability = person goes to Starbucks, get a coffee and doesn't get specialty drink "OR" person goes to Tim Horton's, get a coffee and doesn't get the speciality drink.
= 0.35×.8×(1-.20) + .65×.9(1-.10)
= .35×.8×.8+.65×.9×.9
= 0.224+.5265
= 0.7504
Option D is correct which is between 0.7-0.8.

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