Question

On a summer day, the probability that Anne stays outside for more than 3 hours is 80%. If she stays outside for more than 3 hours, the probability that she gets a sunburn is 65%. If she stays outside for less than 3 hours, the probability that she gets a sunburn is 25%.

(a) Create a sample space for this situation showing all the possibilities.

(b) Anne thinks that the probability of getting a sunburn on a summer day is 60%. Is she correct? Explain your reasoning using probabilities.

Answer 1

let D stay outside for more than 3 hours. Getr a sunburn. then from giren data: P (D) - 0.8 PCD)-1-P1D) = 1-0.8 -0.2 P(Elo -0.65 PCEID) = 0.25 - згі он Sample space for this situation showing all possibilities is { .E/D FlorsjĒ loĒ15} crian Sa res - 0.35 PC @ 1D) PCĒ15) 1-PCE 1D): 1-0,65 l-PCE 15) 1-0, 25 0.75 [ Getting suribum] : p(DAB) P (DAB) =P(END) + Pleno) by using Multiplication theorem. PcEnd). - P(EID).P (D) 0.65 (0.8) PCEND) P (End) PLEID) PCD) 0.25 (0.2) with tambahan ten D) - 0.05 0.52 GS Scanned with Cambclinkein

summen :: PC Getting sunburn on day (B) = P( B DD) + P (DNB ple) = P[END] + pleno) 6.52 to.os... Z 0.57 60 y day is PCE). b] Anne thinks that the prob. of getting sunburn on the summer She is not conect. using the giren probabilities we get the corect ans is. 57 %. because . CSScanned with CamScanner
Thank you.