.1. An urn contains 1 red ball and 10 blue balls. Other than their color, the ba

Question

.1. An urn contains 1 red ball and 10 blue balls. Other than their color, the balls are indistiguishable,
so if one is to draw a ball from the urn without peeking - all the balls will be
equally likely to be selected. If we draw 5 balls from the urn at once and without peeking,
what is the probability that this collection of 5 balls contains the red ball?
2. We roll two fair dice. What is the probability that the sum of the outcomes equals exactly
7?
3. Assume that A and B are disjoint events, i.e., assume that A B = ;: Moreover, let P[A] =
a > 0 and P[B] = b > 0. Calculate P[A [ B] and P[A B], using the values a and b:

Explanation / Answer

1.
P["the red ball is selected"] =
??10
4

??11
5
=
5
11
:
2. There are 36 possible outcomes (pairs of numbers) of the above roll. Out of those, the
following have the sum equal to 7 : (1; 6); (2; 5); (3; 4); (4; 3); (5; 2); (6; 1). Since the dice are
fair, all outcomes are equally likely. So, the probability is
6
36
=
1
6
:
3. According to the axioms of probability:
P[A [ B] = P[A] + P[B] = a + b; P[A B] = P[;] = 0:

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