In a television quiz show Peter answers questions one after another, stopping as soon as a...

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In a television quiz show Peter answers questions one after another, stopping as soon as a question is answered wrongly. The probability that Peter gives the correct answer himself to any question is 0.7. 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. On the first occasion that Peter decides to ask for help he asks the audience. The probability that the audience gives the correct answer to any question is 0.95. This information is shown in the tree diagram below. Peter answers correctly 0.7 0.1 Peter answers wrongly 0.95 Audience answers correctly 0.2 Peter asks for help 0.05 Audience answers wrongly [1] (i) 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. (ii) Find the probability that the first two questions are both answered correctly. [6] (iii) Given that the first two questions were both answered correctly, find the probability that Peter asked the audience. [3] In a television quiz show Peter answers questions one after another, stopping as soon as a question is answered wrongly. The probability that Peter gives the correct answer himself to any question is 0.7. 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. On the first occasion that Peter decides to ask for help he asks the audience. The probability that the audience gives the correct answer to any question is 0.95. This information is shown in the tree diagram below. Peter answers correctly 0.7 0.1 Peter answers wrongly 0.95 Audience answers correctly 0.2 Peter asks for help 0.05 Audience answers wrongly [1] (i) 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. (ii) Find the probability that the first two questions are both answered correctly. [6] (iii) Given that the first two questions were both answered correctly, find the probability that Peter asked the audience. [3]