This document contains examples of probability calculations for events such as coin tosses, card draws from a deck, and committee selections. It also includes examples calculating conditional probabilities, such as the probability of testing positive for diabetes given the accuracy of the test, and the probability of telling the truth given the result of a polygraph test.

1. If a coin is tossed twice, what is the probability
that it will land on "tails" both times?
1 x 1 = 1
2 2 4
If two coins are tossed simultaneously, what is the
probability they will both show "tails"?
Possible outcomes
(H,H) (H,T)
1
(T,H) (T,T) 4

2. Find the probability of getting a face card or a
heart on a single cut of a deck of cards.
P(F or H) = P(F) + P(H) ­ P(F and H)
= 12 + 13 ­ 3
52 52 52
= 22 11
=
52 26

3. Find the probability of getting a face card or a
heart on a single cut of a deck of cards.
Yicong

4. Four cards are dealt from a standard deck of 52
cards. Find the probability that the hand contains
exactly two face cards.
sample space = 52C4
face cards = J, Q, K so 3 x 4 = 12 = 12C2
other 2 cards = 40C2
12C2 . 40C2
P (2 face) = = 0.19
52C4

5. A committee of five shareholders is to be chosen
by lot from seven men and five women. What is
the probability that the committee will consist of
three men and two women?
sample space = 12C5
success = 7C3 x 5C2
7C3 x 5C2 = 175
probability =
12C5 396

6. A test for Type 2 diabetes measures the blood
glucose level after eight hours of fasting. Consider
a blood glucose level above normal to be a
positive result and anything else to be a negative
result. This test is 85% accurate, and 2% of the
world's population actually has diabetes.
Determine P(diabetic tests positive)
hint: draw a tree diagram
0.1037 or 10.3%

8. Polygraph or lie detector test are generally not
very accurate. Suppose a polygraph is 70%
accurate. Assuming that the average person is
truthful 90% of the time. Determine the
probability that a person is telling the truth, given
that the polygraph test indicates truth.
0.954 or 95.4%

9. Good Luck on your
Test tomorrow!!