the probability of joe passing his drivers test is 0.2

He in each question_ What we plan to observe one of the choices but rather the sequence of successes and not the sequence of failutes in his ansu ets, guessing effort. Joe is about to take has not studied for the quiz, s0 he will question multiple-choice Tandomly select quz. 'CHAPTER COUNTING AND PROBABILITY Example 3.2.7. each one being asignmnents of the differ- Assume moreover that the probability_ the probability ent steps are independent of each other Then experiment is the product of an outcome in the whole random the probabilities of the individual steps_' Product Principle for Probabilities Suppose random experiment can be broken down into random experiment 5 On its own quence of steps. u MUMS At this point may be tempted say that the probability of each outcome is 024 but this is wrong because the outcomes are not equally likely: In fact_ in each step the probability of S is smaller than the probability of Fy For each question there are 5 choices_ only one of which is correct: wben Joe guesses randomly the probability of success is 0.2 and the probability of failure is 0.8, in cach question We need something like the product principle for probabilities in order to deal with this: And in fact, there is such principle: [f break down the task of selecting an Outcome into 10 steps, namely the 10 of the selections of S or F, the product principle tells us that there are x2 = 2' = 1,024 outcomes in the sample space. How many different outcomes are there 'n the sample space? 6) What is the probability of each outcome What is the probability of getting cortect and uTonlg ans?ers? If we write each outcome as sequence of Ss and F's failure, respectively each for success and outcome will have exactly 10 letters position there are two choices_ and in each For example_ one outcome SSSSFFSSFS may be written whereas another one may be written as FSSSFSSFSF.

SOLVED: 'CHAPTER COUNTING AND PROBABILITY Example 3.2.7.

The probability of joe passing his drivers test is 0.2