Assignment:
Q1. Suppose you randomly draw two marbles, without replacement from a bag, containing six green, four red and three black marbles.
a) Determine the probability that both marbles are red.
b) Determine the probability that you pick at least one green marble.
Q2. What is the probability of at least two people in a class of 30 students having the same birthday? Assume that no one in the class was born on February 29th.
Q3. A club with eight members from Grade 11 and five members from Grade 12 is electing a president, vice-president and secretary. What is the probability (as a percentage to one decimal place) that Grade 12 students will be elected for all three positions, assuming that all club members have an equal chance of being elected?
Provide complete and step by step solution for the question and show calculations and use formulas.