Answer:
(a) 0.0152%
(b) 1.1663%
(c) 19.4297%
(d) 79.3787%
Step-by-step explanation:
Tickets bought by organizers = 4
Number of tickets = 55
Prizes = 3
(a) The probability that the four organizers win all of the prizes is:
[tex]P = \frac{4}{55}*\frac{3}{54}*\frac{2}{53}\\P=0.0152\%[/tex]
(b) The probability that the four organizers win exactly two of the prizes is:
[tex]P = \frac{4}{55}*\frac{3}{54}*\frac{51}{53}+\frac{4}{55}*\frac{51}{54}*\frac{3}{53}+\frac{51}{55}*\frac{4}{54}*\frac{3}{53}\\P=1.1663\%[/tex]
(c) The probability that the four organizers win exactly one of the prizes is:
[tex]P = \frac{4}{55}*\frac{51}{54}*\frac{50}{53}+\frac{51}{55}*\frac{4}{54}*\frac{50}{53}+\frac{51}{55}*\frac{50}{54}*\frac{4}{53}\\P=19.4397\%[/tex]
(d) The probability that the four organizers win none of the prizes is:
[tex]P = \frac{51}{55}*\frac{50}{54}*\frac{49}{53}}\\P=79.3787\%[/tex]
