Question

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 in set notation.) Y Outcomes 3 4 5 6 7

Answer 1

Step-by-step explanation: Let S represent the sample space , then the possible trials are: S= {SSS, FSSS, FFSSS, FFFSSS, FFFFSSS, …}

Y = the number of trials to be tested.

The possible values of Y are P ={x ∈N , x≥3}

Therefore the five smallest possible values of Y are :

1. Y{SSS} ........ 3 outcomes

2. Y{FSSS} ...... 4 outcomes

3. Y{FFSSS}....... 5 outcomes

4. Y{FFFSSS} ...... 6 outcomes

5. Y{FFFFSSS} ..... 7 outcomes