The Twelve Days of Christmas

The Twelve Days of Christmas

On the first day of Christmas, my true love gave to me:

          A Partridge in a Pear Tree.

If the probability of getting a partridge is .58 and the probability of getting a pear tree is .76, and these are independent events, find the probability of getting a partridge and a pear tree.

On the second day of Christmas, my true love gave to me:

          Two Turtle Doves.

If the probability of a female turtle dove is .53, find the probability of at least one female turtle dove in the pair.

On the third day of Christmas, my true love gave to me:

          Three French Hens.

If the probability of a hen truly having French citizenship is .81, find the probability of exactly two French hens out of the three.

On the fourth day of Christmas, my true love gave to me:

Four Calling Birds.

If the probability of a bird actually calling is .63, find the probability of finding the first calling bird on the third attempt.

On the fifth day of Christmas, my true love gave to me:

Five Golden Rings.

If the probability of getting a real golden ring is .72, find the probability of getting three or fewer golden rings in the five.

On the sixth day of Christmas, my true love gave to me:

Six Geese A-laying.

If the probability of getting an authentic laying goose is .83, find the probability of getting a laying goose on or before the fourth trial.

On the seventh day of Christmas, my true love gave to me:

Seven Swans A-swimming.

If the probability that a swan drowns is .23, find the probability exactly 4 out of the 7 swans drown.

On the eighth day of Christmas, my true love gave to me:

Eight Maids A-milking.

If the probability of getting a sour maid A-milking is .38, find the expected number of sour maids A-milking out of the 8.

On the ninth day of Christmas, my true love gave to me:

Nine Ladies Dancing.

If the probability of a dancing lady accepting an invitation to dance is .18, what is the expected number of ladies you would have to ask, before the first one accepts.

On the tenth day of Christmas, my true love gave to me:

Ten Lords A-leaping.

If the probability of a lame leaping lord is .24, find the probability of getting your first lame leaping lord after the sixth attempt.

On the eleventh day of Christmas, my true love gave to me:

Eleven Pipers Piping.

If the probability of frozen pipes is .63, find the probability of 8 or more frozen pipes out of the 11.

On the twelfth day of Christmas, my true love gave to me:

Twelve Drummers Drumming.

If the probability of a dribbling drummer is .48, find the standard deviation of the dribbling drummers drumming.