Step 1: calculate the probability of rolling a single die and getting a four. Ro

Question

Step 1: calculate the probability of rolling a single die and getting a four. Round the probability to four decimal places

Step 2: Roll a die ten times and record the outcomes. Compile the outcomes and compute the proportion of the rolls that were fours. Round the proportion to four decimal points

Step 3: Roll a die an additional 40 times, for a total of 50 rolls. Combine the outcomes and cmpute the proportion of the rolls that were fours. Round the proportion to four decimal points.

Step 4: Make a chart with on column for "number of fours" and one for "number of rolls". Fill in the chart with the information.

Explanation / Answer

Step1) If we through a die single time then we get sample space is

S={1,2,3,4,5,6}

chance for getting for each number is equal and it is 1/6.

Thus probability of getting 4 is 1/6 = 0.16667

Step2) For this step we generate a R-code as;

x={}

for(i in 1:10)
{
x[i]=floor(runif(1,1,6))
}
x
p=length(x[which(x==4)])/length(x)
p

Thus p gives us proportion of 4 in 10 times die is rolled.

Here given my outcome as;

{1,4,1,5,2,2,2,2,1,4}

And the proportion of 4 is 2/10 = 0.20000

step3) The r-code is as;

x={}
for(i in 1:50)
{
x[i]=floor(runif(1,1,6))
}
x
p=length(x[which(x==4)])/length(x)
p

Here my observations are(i.e. my outcome is)

> x
[1] 2 1 5 4 5 3 4 3 2 1 5 3 3 3 3 4 4 3 5 4 2 1 1 2 1 4 2
[28] 5 1 5 2 2 1 1 1 2 4 2 2 5 2 3 3 4 3 2 4 2 1 3
> p=length(x[which(x==4)])/length(x)
> p
[1] 0.18

here p gives proportion of 4 in 50 times die rolled.

thus the proportion of 4 in 50 times die rolled is 0.1800

step 4) The table is given below;

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