Question:
(a) Jonka tries to connect to his internet service provider. The probability that he connects on any single attempt is 0.85 .
(i) What is the probability that he connects for the first time on his second attempt?
(ii) He decides to attempt only three times to connect to his internet. List all possible outcomes and draw a suitable tree diagram to represent this experiment.
(iii) What is the probability that he is still not connected after his third attempt?
(b) A particular binomial distribution, X ∼ B(n, p) has the mean 4 and variance 3.
(i) Find the values of n and p.
(ii) Find the probability, P(6 ≤ X ≤ 8) close to four dp using your calculator. Check your answer with R and give the corresponding command/s together with the output and answer.
(c) In a game, three regular, six-sided dice are thrown once. Find the probability of observing three different numbers. A player claims that you expect to see three different numbers on the dice in at least half of the games. Is the player correct? Justify your answer.