Answer:
(a) P = 0.0001
(b) P = 0.6561
(c) P = 0.2916
(d) P = 0.3439
(e) P = 0.2
Step-by-step explanation:
This is a probability problem.
The dice is rolled 4 times (n=4) and we calculate the probability of different outcomes.
The probability of a 6 in a roll is 0.5.
The probability of a 1, 2, 3, 4 or 5 in a roll is 0.5/5=0.1.
<u />
<u>a) Outcome: all the rolls are 2.</u>
The probability of having a 2 in a roll is 0.1, so we can calculate the probability of having a 2 in four consecutive rolls as
<u>b) Outcome: none of the rolls is a 2.</u>
The probability of having any other number but 2 in 4 rolls is:
<u>c) Outcome: exactly one roll is a 2</u>
This is the sum of the probability of having a 2 in the first, second, third or fouth roll, and others numbers in the rest of the rolls. These 4 combinations have the same probability, so we will multiply it by 4.
<u>d) Outcome: at least one of the rolls is a 2</u>
In this case, is the probability of having at least one 2, is the sum of the probability of getting a 2 in the first roll, the probability of getting a 2 in the second roll, the probability of getting a 2 in the third roll and the probability of getting a 2 in the four roll:
<u>e) Outcome: either the first roll or the last roll is a 2</u>
The probability of getting a 2 in the first roll is equal to having it in a fourth roll, and its the probability of getting a 2 in a roll (multiplied by 2, beacuse there can be either in the first or in the last roll).