Mathematics, 21.06.2021 06:40 gui00g7888888888888

A fair six-sided die is thrown four times Find the probability, correct to three decimal places, of getting i) exactly one six occurs
ii) at least one six occurs

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Answer from: jabezslade22

I) 0.386 = 38.6% probability that exactly one six occurs.

II) 0.518 = 51.8% probability that at least one six occurs.

Step-by-step explanation:

For each throw, there are only two possible outcomes. Either it is a six, or it is not. The probability of a six being rolled is independent of other throws, which means that the binomial probability distribution is used to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

In which $C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

And p is the probability of X happening.

Thrown four times

This means that n = 4

Probability of rolling a six:

Six sides, one of which is 6. So

$p = \frac{1}{6} = 0.1667$

i) exactly one six occurs

This is P(X = 1) . So

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 1) = C_{4,1}.(0.1667)^{1}.(0.8333)^{3} = 0.386$

0.386 = 38.6% probability that exactly one six occurs.

ii) at least one six occurs

This is:

$P(X \geq 1) = 1 - P(X = 0)$

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 0) = C_{4,0}.(0.1667)^{0}.(0.8333)^{4} = 0.482$

$P(X \geq 1) = 1 - P(X = 0) = 1 - 0.482 = 0.518$

0.518 = 51.8% probability that at least one six occurs.

Answer from: Quest

she was supposed to add the hours(38.5) and multiply the amount of money she earned(7.50) resulting in $288.75 .

correct me if i'm wrong and if it is i'm truly sorry.

Answer from: Quest

First, think of what you know. you know that the number t the end of the equation will need to be subtracted because it is the money he lost from buying the lawn mower. and your first two weeks have negative profit, so that tells you that c and d are wrong. now you can plug any of the weeks into a and b to see which one works. i'll start with plugging week 1 into a. $y = 60(1) - 90 \\ y = 60 - 90 \\ y = - 30$ this isn't right because it says your answer for week one should be -90.so now we need to try the same thing with b. $y = 60(1) - 150 \\ y = 60 - 150 \\ y = - 90$ this one got you the right answer, (sometimes if you only check with one of the weeks multiple will work so you need to check with more of the weeks, but it worked out fine here)this means that b is the correct answer.let me know if you need more clarification. i hope this : )

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