Question

In the case of a game of chance, every 20th person usually wins an amount of more than EUR10000. How many players have to compete so that with a probability of 95% at least one more than ¨ EUR 10,000 wins?

In a large sports competition, the participants are checked for doping. Experience has shown that 4 out of 75 participants consume illicit substances. A test should check whether the athlete ¨
fights fairly. It is known that this test has a probability of 0.97 to convince a doped athlete as such. However, 2% of athletes are also wrongly accused of doping by the test. What is the probability that a positive athlete actually doped?

Answer 1

proportion of doped participants – 1/5 PD) proportion of otoped Plaad= 1- P10)=1-4 / 4 = 2/15 The test result of test P ( positive / poped Athlet) = P(P/D)=0.97 P ( positive / Not Doped Athlet)= P(P/ND) = 2%= 0.02 Tree -diagram: positive PID) PCP/D) 0.97 poped Test Negative 1-0.97 -0.03 PIND) particant Not Doped P(P/ND) -positive 0.02 71 75 PEND) Test 1-0.02=0.98 PININD) Negative - Goom The probability that a positive athlete actually doped PD). Piplo) =P(DIP) (theorem PD) P(PID) + P (ND). P(P)ND) 6X0-97) = 10.732675 ( x 0.91)+( 7x002) 0.07066667 (Upto 6 decimels) 0.05173333 :. The probability is 10.7321 up to 4 decimas .