4 dice rolled probability of not getting same number on 3 dices?
Answers
4 dice rolled probability total number of outcomes is 6 x 6 x 6 x 6
probability of not getting same number on 3 dices be P(E)
Therefore P(E)= 1- probability of getting same number on 3 dices,P(A)
The numbers in a die be 1, 2, 3, 4, 5 and 6
the possible outcomes of getting 3 numbers same is 4c3 =4
AAAB, AABA, ABAA, BAAA
The number A be 1 to 6 and number B be 1 to 6
total possibilities of getting 3 numbers same are 4 x 6 x 6
P(A)= (4 x 6 x 6)/(6 x 6 x 6 x 6) = 1/9
probability of not getting same number on 3 dices be P(E) = 1 -P(A) = 1- 1/9 =8/9
Total number of outcome per dice = 6
P(getting the same number as another throw) = 1/6
Find the probability of getting 3 of the same number:
Probability of getting 2 of the dice the same as one of the other 2:
= 1 x 1 x 1/6 x 1/6
= 1/36
Find the number of ways this can happen:
Number of ways to get 3 out of the 4 dices the same :
= 4C3
= (4x3x2x1)/(3x2x1)
= 4
Find the probability of getting 3 of the same:
P(3 of the same) = 1/36 x 4 = 1/9
Find the probability of NOT getting 3 of the same:
P(getting 3 NOT the same) = 1 - P(getting 3 of the same) = 1 - 1/9 = 8/9
Answer: 8/9