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dee21099
06.10.2019 •
Mathematics
Answers should be exact decimals ( do not leave as fractions or unfinished calculations). a six-sided die (cube) with faces numbering 1,2,3,4,5,6 is loaded so that the probability of a six is 1/2. all the remaining numbers are equally likely.1) we roll the loaded die four times. find the probability ..all the rolls are 2: none of the rolls are 2: exactly one of the rolls is a 2: at least one of the rolls is a 2: either the first roll or the last roll is a 2:
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Ответ:
(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.
a) Outcome: all the rolls are 2.
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
b) Outcome: none of the rolls is a 2.
The probability of having any other number but 2 in 4 rolls is:
c) Outcome: exactly one roll is a 2
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.
d) Outcome: at least one of the rolls is a 2
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:
e) Outcome: either the first roll or the last roll is a 2
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).
Ответ:
Break the figure into a parallelogram and a triangle. Find the area of each using the formulas A=bh and A=1/2bh. The sum of the areas is the area of figure.