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​

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.

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

And p is the probability of X happening.

Thrown four times

This means that

Probability of rolling a six:

Six sides, one of which is 6. So

i) exactly one six occurs

This is . So

0.386 = 38.6% probability that exactly one six occurs.

ii) at least one six occurs​

This is:

So

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

option a is correct.

step-by-step explanation:

scale factor: it is used to find proportional measurements.

proportions means having the same ratio.

scale factor is the ratio of the model measurement to the actual measurement in a simplest form.

or we can say that the ratio of any two corresponding lengths in two similar geometric figures

if the scale factor is more than 1, then it is an enlargement,

if the scale factor less than 1, then it is a reduction.

given the two geometric figure:

by definition of proportions, we have

probably the last option

step-by-step explanation: