In: Statistics and Probability
Please show all steps:
A: Suppose that 90% of adults with allergies report symptomatic relief with a specific medication. If the medication is given to 10 new patients with allergies, what is the probability that it is effective in exactly six?
B: A small voting district has 110 female voters and 90 male voters. A random sample of 10 voters is drawn. What is the probability exactly 8 of the voters will be female?
C: A deck of cards contains 30 cards: 10 red cards and 20 black cards. 5 cards are drawn randomly without replacement. What is the probability that exactly 3 red cards are drawn?
D: The bivariate probability distribution of X and Y is given in the table below.
x | 2 | 4 | 6 |
3 | .1 | .2 | .1 |
5 | .15 | .25 | .2 |
What is the conditional probability that X=3 given that Y=2?
Are X and Y independent? Explain