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))

answer: translate the circles so they share a common center point and dilate circle y by a scale factor of 3.