Question

On any given day, the probability that Stacy uses the map app on her phone at some point during the day is 30%. The chance of Stacy's phone dying by the end of the day is 25%. However, she has noticed that on the days she uses the map app, there is a 40% chance of her phone dying by the end of the day. What is the probability that, on any given day, Stacy's phone eventually dies and she has used the map app.

A. 0.10
B. 0.08
C. 0.15
D. 0.12​

Answer 1

The probability that Stacy's phone will die on a day she uses the map app is 12% (0.12), which is found by multiplying the probability of using the app (30% or 0.3) by the conditional probability of the phone dying given the app is used (40% or 0.4).

Step-by-step explanation:

The question asks to calculate the probability that Stacy's phone will die on a given day given she has used the map app. To calculate this, we need to use the information given about the probabilities of individual events and their conditional probabilities. The probability of Stacy using the map app is 30% (or 0.3), and the probability of her phone dying on those days is 40% (or 0.4).

We find the joint probability of both events happening by multiplying the probability of Stacy using the map app by the probability of her phone dying given that she uses the app:

Probability(Phone dies and uses map app) = Probability(Uses map app) × Probability(Phone dies | Uses map app)

0.3 × 0.4 = 0.12

Therefore, the probability that Stacy's phone eventually dies and she has used the map app on any given day is 0.12 or 12%. The correct answer is D. 0.12.