Question

The landing time of Madame Sophie Blanchard (eminent French balloonist) on a field just outside of Compiègne is uniformly distributed on the interval (1PM, 2PM). Her nemesis, Monsieur Guy LeBoeuf (pronounced Gee Luh-Buhf) independently lands his balloon on the same field at a time that is also uniformly distributed on (1PM, 2PM). Determine the probability that the first to land does so prior to 1:15 PM (draw a picture). the answer is 0.4375

I would like to know the answer of question 24

In problem (23), determine the probability that the first to land does so prior to 1:15 PM, given that both Mme Blanchard & the despicable LeBoeuf land prior to 1:45.

a) 7/9 b) 1/3 c) 1/2 d) 5/9 e) 2/3

Answer 1

1) probability that the first to land does so prior to 1:15 PM =1-P(none of them goes prior to 1:15 PM)=1-(45/60)*(45/60)=0.4375

2)

P(both goes prior to 1:45) =(45/60)*(45/60)=0.5625

P(both goes prior to 1:45 and at least one goes prior to 1:15)=P(both prior to 1:45)-P(both from 1:15 to 1:45)

=0.5625-(30/60)*(30/60)=0.3125

therefore probability that the first to land does so prior to 1:15 PM, given that both Mme Blanchard & the despicable LeBoeuf land prior to 1:45 =0.3125/0.5625=5/9