A three-dice is a six sided dice with only the numbers 1, 2 and 3. The usual numbers 4, 5 and6 are replaced by 1, 2 and 3 respectively.
4 three-dice (with sides labeled 1, 2, and 3) are rolled and the numbers face up on the 4 dice
are recorded. Give the sample space for this experiment. What is the probability that at least
one of the dice rolled is showing a 2?
What is the probability that at least one of the dice rolled is showing a 2?=

Answers

Answer 1

Answer:

The sample space for the experiment N(S) = 12 and the probability of showing 2 on at least one die is 41/81.

What is probability?

Probability is the chance of occurrence of a certain event out of the total no. of events that can occur in a given context.

Given that four three-sided dice(4, 5, 6 are replaced by 1, 2, 3) are rolled.

As each die has two 1's, two 2's, and two 3's the no. of distinct sample space N(S) each die has is 3, and there are a total of four dice so the total no.of sample space is (3×4) = 12.

∴ The probability that one of the die is showing 2 is (2/6) = 1/3.

So, the probability that at least one of the die is showing two is sum of one die showing two to sum of 4 dice showing 2 which is,

= 2/6 + (2/6)(2/6) + (2/6)(2/6)(2/6) + (2/6)(2/6)(2/6)(2/6).

= 1/3 + 1/9 + 1/27 + 1/81.

= (27 + 9 + 3 + 1)/81.

= 40/81.

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Answer 2

Answer: Over all it’s still a 1/3 of getting a 2 when rolling

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