Find the probability distribution of the number of sixes in a simultaneous toss of three dice.

Asked by Aarthi Vishwanathan | 23rd Dec, 2013, 06:50: PM

Expert Answer:

A six can be obtained in one of the dice, two of the dices or all 3 of the dices.
Let P(X) represent the probavility of getting x sixes in a throw of 3 dice.
 
Probability of getting 1 six. That is, P(1) :
 
Probability of obtaining a six in one dice is 1/6.
Since a six can be obtained in the first, second or the third dice, probability of
getting 1 six in a throw of 3 dices is : 1/6 + 1/6 + 1/6 = 3/6 = 1/2.
 
Probability of getting 2 sixes. That is, P(2) :
 
Probability of obtaining sixes in 2 dice is (1/6) X (1/6).
2 dices can be chosen from 3 dices in 3C2 =  3 ways.
Thus, the probability of getting 2 sixes in a throw of 3 dices is :
3 X (1/6) X (1/6) = 3/36 = 1/12.
 
Probability of getting 3 sixes. That is, P(3) :
 
Probability of obtaining sixes in all 3 dice is (1/6) X (1/6) X(1/6).
There is only one way in which 3 dice can be chosen from 3 dice.
Thus, the probability of getting 3 sixes in a throw of 3 dices is :
(1/6) X (1/6) X (1/6) = 1/216.
 
Thus, the probability distribution is :
 
X             1          2         3
P(X)     1/2       1/12    1/216
 
 
 
 

Answered by Vimala Ramamurthy | 24th Dec, 2013, 08:41: AM

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