Each time a component is tested the trial is a success (S) or failure (F). Suppose the component is tested repeatedly until a success occurs on three consecutive trials. Let Y denote the number of trials necessary to achieve this. List all outcomes corresponding to the five smallest possile values of Y, and state which Y value is associated with each one. Y Outcomes
3
4
5
6
7

Step-by-step explanation:

Given

Success

Failure

Consecutive trials until S happens

Number of trials

For every possible outcome, the last 3 must be SSS. So, we have:

The only possibility here is:

because 3 trials implies that all outcomes must be S.

The only possibility here is:

because 4 trials implies that the first outcome must be F

The possibilities are:

because 5 trials implies that the first and the second outcomes must be FS or SF.

The possibilities are:

because 6 trials implies that the first three outcomes are: FFF, SSF and SFF

The possibilities are:

because 7 trials implies that the first three outcomes are: FFFF, FSSF and SSFF and FFSF (similar to (e))

d

step-by-step explanation:

hello and welcome!

so, when we see the words "proportional" along with a table, we need to know that we're looking numbers that divide by the same thing.

looking at this table, we simply have to do a trial and error, and divide to see which numbers have the same quotient. if you look at choice a & c, they both have equal quotients for three of the numbers, with one exception, so those can't be the answer. looking at b, there is no similarity, so that can't be it. then, we see d; if you divide all the numbers in the table, you'll see that they all divide by two, which is a proportional relationship, and our answer!

also, always remember that the x will always be the number that goes into y, and somewhere behind this table, is a formula. for this specific table, the formula would be:

since our x-value is being divided by two to get the y-value. and if they were to ask for more numbers in the series, this is the formula you would use to find them.

table a is wierd

step-by-step explanation:

6*f