help needed urgent (1 Viewer)

[Petinga]

1. In each game of sic bo, three regular, six sided dice are thrown once.
a)In a single game, what is the probability that exactly two dice show a 2.
b)what is the probaility that exactly 2 of the dice show the same number
c) a player claims that you expect to see three different numbers on the dice in at least half of the games. Is the player correct? justify your answer

 

[Riviet]

(a) total number of outcomes = 6³ = 216

number of ways of getting exactly 2 on 2 die = 3C2 = 3

.'. probability = 3/216 = 1/72

(b) From part (a), this is the probability for getting two 2's on any two die. We want the probability for getting two of any of the 6 numbers on any two die. So I think we just use part (a)'s answer and multiply 1/72 by 6, which equals 1/12.

(c) When we throw the first dice, it can be any of the 6.
When we throw the second dice, since it can't be the same as the first, there are only 5 possibilities.
When we throw the third dice, since it can't be the same as the first or second die, there are only 4 possibilities.
Since these events occur at the same time, the total number of ways of 3 different numbers on the three die = 6 x 5 x 4 = 120.

.'. probability = 120/216 = 0.55, (2 decimal places) which is close to half of the games.

Hence the player is correct in making that statement.