How do I solve questions 2a, 2b, and 2c. Please show work

2. County C needs to construct an n - 3 person jury. The population of C has two types of jurors, H types, which favor the prosecution, and _ types, which favor the defense. The population is 2/3 H types, and 1/3 L types. (a) If a jury is randomly selected from the population, how many H and L types would sit on it (be "impaneled") in expectation? (b) If the jury is randomly selected from the population, what is the probability that it is composed of all H types? (HINT: each draw from the population is independent and has probability 2/3 of being an H type, so the question is what is the probability of drawing 3 consecutive H types) (c) If each side in the trial gets I peremptory challenge, then @ must draw 5 potential jurors from the population. The jury will be all H types if - 1 of these S is type I. The probability that exactly I is type L is: 80 243 Calculate the probability that there are 0 type L jurors in the pool (thus the pool is 5 type H; this is calculated in an analogous way to part (a) for a draw of 3 type H jurors). Add these two probabilities together to get the probability that the impaneled jury is all type H. Is this probability greater than or lower than the probability you found in (a)?(d) Your answer for (c) should be that the probability is higher than in (a). Given this, briefly discuss whether you think peremptory challenge increase or decrease the likelihood of achieving a representative cross section of society on the jury