Any help would greatly be appreciated.
In a lotto, each week 5 balls are selected at random, without replacement,
from an urn that contains 39 balls numbered 1, 2,...39. A player bought a
ticket with his choice of 5 different numbers. If all 5 of the numbers
drawn from the urn match the player's numbers, then he is a Big Winner. If
exactly 4 of the 5 numbers drawn from the urn match 4 of the player's
numbers, then he is a Little Winner. Suppose that John buys a ticket with
the numbers 1, 2, 3, 4, 5; and suppose that Mary buys a ticket with the
numbers 2, 3, 4, 5, 6.
1. Find the probability that John and Mary will have at least
one Big Winner or Little Winner ticket between them.
Consider two dice, each with faces colored red, white, or blue. One of
the dice is colored red on the faces numbered 1 and 6, white on faces 2
and 5, and blue on faces 3 and 4; the other die is red on faces 1, 2, 3,
and 4, white on face 5, and blue on face 6. Suppose that one of the dice
is chosen at random and rolled 10 times, and then the remaining die is
rolled 10 times.
2. Find the probability that the second die will produce the
same sequence of colors as the first.
3. Suppose that the first roll of the first die produces a red
face. Find the probability that the first roll of the second die
will also be red.
