Globokim8

2020-12-29

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?

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?

Talisha

Skilled2020-12-30Added 93 answers

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$7\text{}\Rightarrow \text{}7$ 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$\Rightarrow \text{}5$ ways

And in remaining 4 rolls, any outcome can come$\Rightarrow {7}^{4}$ ways

Total favourable ways$=5\text{}\times \text{}{7}^{4}$

Probability$=(5\text{}\times \text{}{7}^{4})/{7}^{5}$

$=5/7$

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

$=1\text{}-\text{}(probability\text{}of\text{}3\text{}is\text{}never\text{}rolled)$

So 3 should never come$\Rightarrow $ possible outcomes are 1, 2, 4, 5, 6, 7

Number of ways$=6$

For five time rolls$={5}^{6}$

Probability$=1\text{}-\text{}({5}^{6}/{5}^{7})$

$=1\text{}-\text{}(1/5)$

$=4/5$

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$\Rightarrow \text{}2,\text{}4,\text{}6,\text{}\Rightarrow $ 3 outcomes

So 4 rolls even$={4}^{3}$ ways

And remaining one roll in 7 ways

Total favourable ways$=7\text{}\times \text{}{4}^{3}$

Probability$=(7\text{}\times \text{}{4}^{3})/{7}^{5}$

\(= 64/2401

Hence the probability that exactly 4 of the rolls show even number.

(Rounded to 3 decimals)

Given a fair 7-sided die with numbers 1 to 7.

It is rolled 5 times.

So total number of outcomes

as one time rolled can give any number from 1 to

So five time rolled

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

And in remaining 4 rolls, any outcome can come

Total favourable ways

Probability

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

Number of ways

For five time rolls

Probability

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

So 4 rolls even

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)

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