Calculate the following probabilities. Round to the thousandth. Use 0+ if necessary.
a) Assume you roll fair die three times. How likely is it you will get a on all three rolls (that is, a one on the first roll, a one on second roll and a one on the third roll)?
b) Assume that 30% of plain M&Ms are brown. If you choose 4 M&Ms at random, how likely is it you will get at least one brown?
c) Assume you choose a person at random. Supposing birthdays are uniformly distributed during the year, how likely is it that person will have his or her birthday upon a day of month that is divisible by 5 (like on the 5th, the 10th, the 15th, ...)? (Disregard leap year.) Be as exact as possible.
d) If you choose a single card from standard deck of 52 cards, how likely is it the card will be heart or a face card (queens, kings and jacks are considered face cards)?
e) Assume a couple decides to have four children. How likely is it the couple will have one girl and three boys, in any order? Suppose any single baby is equally likely to be the boy or a girl.