An otherwise fair six-sided die has been tampered with in an attempt to cheat at a dice game. The effect is that the 1 and 6 faces have a different probability of occurring than the 2, 3, 4 and 5 faces. Let 0 be the probability of obtaining a 1 on this biased die. Then the outcomes of rolling the biased die have the following probability mass function.

(6) An otherwise fair sir sided die has been tampered with in an attempt to cheat at a dice game. The effect is that the 1 and 6 faces have a different probability of occurring than the 2, 3, 4 and 5 faces. Let ở be the probability of obtaining a 1 on this biased die. Then the outcomes of rolling the biased die have the following probability mass function. Table 1 The p.m.f. of outcomes of rolls of a biased die Outcome 1 2 3 4 5 6 Probability 0 (1- 20) (1 – 20) (1– 20) {(1 – 20) 0 Heeessary (ii) The value of 0 is unknown. Data from which to estimate the value of 0 were obtained by rolling the biased die 1000 times. The result of this experiment is shown in Table 2. Table 2 Outcomes of 1000 independent rolls of a biased die Outcome 1 3 4 5 6. Frequency 205 154 141 165 145 190 Show that the likelihood of 0 based on these data is L(0) = C0395 (1 – 20)605, where C is a positive constant, not dependent on 0. (iii) Show that Stare what rule is ased, L'(0) = C 6394 (1 – 20)®04 (395 – 2000 6).…

A randomly selected car owner in New York might be having a Japanese made car, where the probability of this event is 0.4. The same person might be having an American made car, where the probability of this event is 0.2. The probability that the same person is having cars of both origins is 0.1. Find the probability that the diver is New York has the car of Japensese origin, but not the American origin.

The probability that a machine develops a fault within the first 3 years of use is 0.003. If 40 machines are selected at random, the probability that 38 or more will not develop any faults within the first 3 years of use is ....