Please show all working . Please show all working . Please show all working . 5.

Question

Please show all working . Please show all working . Please show all working . 5. In a television quiz show Peter answers questions one after another, stopping as soon as a question is answered wrongly . The prubahility that Peter gives the correct aimwer himself to any question ?s 07. The probability that Peter gives a wrong answer himself to any question is 0.1 The probability that Peter decides to ask for help for any question is 0.2. 0 the fint occasion that Peter decides to ask for help he asks the incience. The probability that the sudience gives the correct answer to any question is 0.95. This information is shown in the tree diagram below Peter anewers cornectly 0.7 0.1 Peter amwen wrongly 0.95 Auudience answers correcty 0.2 Peter asks for help 5Audience answers wrongly h Show that the probability that the first question is answered correctly is 0.89 On the second occasion that Peter decides to ask for help he phones a friend. The probability that his friend gives the correct answer to any question is 0.65 il) Find the probability that the first two questions are both answered correcily ili) Given that the first two questions were both answered correctly, find the probability that Peter 16) asked the audience. 131

Explanation / Answer

i)

P(first question is answered correctly) =P(he answers correctly himself) +P(he asks for help and answers is correct)

                                                        =0.7 + 0.2*0.95

                                                        =0.7+0.19

                                                        =0.89

ii)

P(both questions are answered correctly) = P(first question is answered correctly) * P(second question is answered correctly)

P(first answer is correct) =0.89

P(second answer is correct) = 0.7 + 0.2*0.65

                                              =0.7 + 0.13

                                              =0.83

So,P(both questions are answered correctly) = 0.89 * 0.83

                                                                          = 0.7387

iii)

P(Peter asks audience | he answered both correctly) = P(Peter asks audience and he answered both correctly)/P(he answered both correctly)

                                                                                        = (0.2*0.95)/0.7387

                                                                                        =0.19/0.7387

                                                                                        =0.2572                                                                                             

                                                                                   

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