 # Marks will be awarded for accuracy in the rounding of final answers where you are asked to round. To ensure that you receive these marks, take care in Globokim8 2020-12-29 Answered
Marks will be awarded for accuracy in the rounding of final answers where you are asked to round. To ensure that you receive these marks, take care in keeping more decimals in your intermediate steps than what the question is asking you to round your final answer to.
A fair 7 -sided die with the numbers 1 trough 7 is rolled five times. Express each of your answers as a decimal rounded to 3 decimal places.
(a) What is the probability that exactly one 3 is rolled?
(b) What is the probability that at least one 3 is rolled?
(c) What is the probability that exactly four of the rolls show an even number?
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Data analysis
Given a fair 7-sided die with numbers 1 to 7.
It is rolled 5 times.
So total number of outcomes $={7}^{5}$
as one time rolled can give any number from 1 to out comes
So five time rolled $={7}^{5}=16.807$
To find the following probabilities.
Sub part a)
Probability that exactly one 3 is rolled.
One 3 can come in any of the 5 rolls ways
And in remaining 4 rolls, any outcome can come $⇒{7}^{4}$ ways
Total favourable ways
Probability
$=5/7$
Hence the probability that only one 3 is rolled is 0.714
(Rounded to 3 decimals)
Sub part b)
Probability that at least one 3 is rolled

So 3 should never come $⇒$ possible outcomes are 1, 2, 4, 5, 6, 7
Number of ways $=6$
For five time rolls $={5}^{6}$
Probability

$=4/5$
Hence the probability that atleast one three is rolled is 0.8
Sub part c)
Probability that exactly 4 of the rolls show even number.
Even number 3 outcomes
So 4 rolls even $={4}^{3}$ ways
And remaining one roll in 7 ways
Total favourable ways
Probability
\(= 64/2401
Hence the probability that exactly 4 of the rolls show even number.
(Rounded to 3 decimals)