Oppgaven er:
Jeg var litt usikker på hva "false positive" betyr, så det var bra fasiten klarnet det opp først:Weightlifters
A coach has two teams - the Cleaner team ($C$) and the Steroid team ($S$). He sends one of the two teams for competition. Each team has 10 members. Eight members of the Steroid team ($S$) use steroids. Two members of the Cleaner team ($C$) use steroids. The coach chooses which team to send for competition by tossing a fair coin.
One athletics committee tests for steroids in the urine of only one randomly chosen member of the team that has been sent. The test is 100% effective. If this team member is a user ($U$), the team is rejected.
a)
What would be a false positive rejection of the entire team?
b)
What is the probability of a false positive?
c)
Another committee is more rigorous. It randomly chooses two different members. What is the probability of a false positive?
Da burde jo b) være enkel. For at det skal være en false positive, må altså the Cleaner team være sent, og en steroidebruker være plukket ut derfra.(a)
The coach sent the Cleaner team, but the committee randomly selected a user, and decided that the Steroid team had been sent.
$P(C & U) = P(C) \cdot P(U | C) = 0.5 \cdot 0.2 = 0.1$
Fasiten sier 0.2.
Jeg er heller ikke enig i c). Hva får dere der?
Takk for innspill!