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 possible values of Y. (Enter your answers as a comma-separated list.)Y Outcomes

a. 3b. 4c. 5d. 6e. 7

a) Y = 3 trials : [SSS]

b) Y = 4 trials : [FSSS]

c) Y = 5 trials: [FFSSS; SFSSS]

d) Y = 6 trials: [FFFSSS; SSFSSS; SFFSSS; FSFSSS]

e) Y = 7 trials: [SSS; FFSFSSS; FSSFSSS; SSFFSSS; SFSFSSS; SFFFSSS; FSFFSSS]

Step-by-step explanation:

Here the outcome of a trial is S(success) or F(failure). We are told the component is tested repeatedly until a success occurs on three consecutive trials, which means an outcome of S must be gotten 3 time consecutively (SSS).

Let's take Y as the number of trials, therefore

a) Y = 3 trials : [SSS]

This outcome is the only possibility here because we are limited to just 3 trials and S must happen 3 times consecutively.

b) 4 trials : [FSSS]

Similar to option A, S should be gotten an 3 consecutive trials.

c) 5 trials: [FFSSS; SFSSS]

In this case F is also possible, but if we get FSSS there would be no need for a fifth trial since we have gotten 3 consecutive S.

d) 6 trials: [FFFSSS; SSFSSS; SFFSSS; FSFSSS]

In this case the 4 last outcomes must be FSSS. For the outcomes before the last 4, we just had to make sure it doesn't have S 3 consecutive times

e) 7 trials: [SSS; FFSFSSS; FSSFSSS; SSFFSSS; SFSFSSS; SFFFSSS; FSFFSSS]

This is similar to option d

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step-by-step explanation: