You have a fair dice and you roll it thrice. You are interested in the total (su

Question

You have a fair dice and you roll it thrice. You are interested in the total
(summation) of the three outcomes. Let A = Event that we get an odd value after summing the
outcomes of the dices, B = Event that we get a value greater than 8 after summation of outcomes. C =
Event that the summation of outcomes is an even value. Using this information answer the following
questions:
after calculating the sample space , please answer the following questions:
a. Calculate the probability that you get an odd value given that only one of the dice value is
greater than or equal to 4.
b. Calculate the probability that you get an odd value given that only two of the dice values are
greater than or equal to 4.
c. Calculate the probability that you get an odd value given that all the dice values are greater
than or equal to 4.
d. Calculate the probability that you get an odd value given that the summation of the dice values
is greater than or equal to 14.

Explanation / Answer

a) given that on 1 dice its >= 4

let at one dice its 4

all possibilities to get odd ( 4,11) (4,1,3) (4,1,5) ,(4,2,1) (4,2,3) (4,2,5) ,(4,3,2),(4,3,4),(4,3,6),(4,4,1),(4,4,3),(4,4,5)

(4,5,2),(4,5,4),(4,5,6),(4,6,1)(4,6,3),(4,6,5)

total 18

if at dice its 5 then same as all possibilities 18 and same as with 6

total possibilities is 3*18

p(odd) = 3*18/63 =0.25

b)

b) same as a) we can calculate all possibilities

if first apear 4

(4,4,1) (4,4,3),(4,4,5), (4,5,2,(4,5,4),(4,5,6)

same thing will happen with 5 and 6

all possibilities

3*6   

p = 3*6/63 =0.083

c) all possibilities

( 4,4,5),(4,5,4),(4,5,6),(5,4,4),(5,4,6),(5,5,5),(5,6,6),(6,4,5) (6,5,4),(6,5,6)

att possibilities=10

p=10/63 =0.0463

d)

all possibilities ( 4,5,6),(4,6,5)( 5,4,6) (5,5,5),(5,6,4),(6,4,5),(6,5,4) (6,6,5)

p= 8/63 =0.037

thanks

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