CAIE S1 2015 June — Question 4

Exam BoardCAIE
ModuleS1 (Statistics 1)
Year2015
SessionJune
TopicTree Diagrams
TypeFind unknown probability parameter

4
\includegraphics[max width=\textwidth, alt={}, center]{c0c7e038-805a-4237-a579-a6571b84f337-2_451_1530_1393_303} A survey is undertaken to investigate how many photos people take on a one-week holiday and also how many times they view past photos. For a randomly chosen person, the probability of taking fewer than 100 photos is \(x\). The probability that these people view past photos at least 3 times is 0.76 . For those who take at least 100 photos, the probability that they view past photos fewer than 3 times is 0.90 . This information is shown in the tree diagram. The probability that a randomly chosen person views past photos fewer than 3 times is 0.801 .
  1. Find \(x\).
  2. Given that a person views past photos at least 3 times, find the probability that this person takes at least 100 photos.