Finite Math Computing Probabilities By Using Equally Likely Outcomes http://finitehelp.com/

1. 2.4
Computing Probabilities By Using Equally Likely Outcomes

2. Calculating Probabilities
 This section combines what you learned from 2.1-2.3
 In 2.1, you learned that if there are n elements
equally likely in the sample space, then each element
has probability 1/n.
 In 2.2 and 2.3, you learned how to determine the
number of elements in counting arrangements of
permutations and combinations
 Therefore, the probability of an event is the number of
elements in the event, divided by the number of
elements in the sample space, given each element is
equally likely (which will be in problems you encounter
in this class)

3.  Let’s do an example. I have 7 coins (2 dimes and 5
quarters). I select 2 at random. What’s the probability that
they are both quarters?
 We need two pieces of information here: # of elements in
the event of drawing 2 quarters, and the # of elements in the
sample space of draw any two coins.
 This is a combination problem.
# elements (2Q) = C(5,2) = 10 (2Q out of 5)
# elements (any 2 coins) = C(7,2) = 21 (2 coins out of 7)
Therefore: Pr(2Q) = [# element (2Q)]/[# element SS] = 10/21

4. Quiz 2.4 #1
 An urn has 7 balls – 4 red and 3 green. Jimmy
picks 3 balls from the urn. What is the
probability that all 3 are red?
A. 1/35
B. 4/35
C. 10/35

5. Quiz 2.4 #1
 An urn has 7 balls – 4 red and 3 green. Jimmy
picks 3 balls from the urn. What is the
probability that all 3 are red?
A. 1/35
B. 4/35
C. 10/35
 Answer: B

6. More advanced problem
 Remember from 2.3 you learned about
calculating elements with multiple pools and
multiple scenarios. Let’s put that to use with
calculating probabilities.
 Harry and Sally are auditioning for a play along
with 4 other males and 2 other females. The
play requires 3 distinct male roles and 2 distinct
female roles. If the actors are selected at
random, what is the probability both Harry and
Sally are chosen?

7.  This is a permutation problem with multiple pools. I will be
using the slot method to solve this:
 To determine the probability of an event, again we’ll use the
formula:
 # of elements in event (Harry is in, Sally is in)
H(1) x 4 x 3 x S(1) x 2 = 24
Since Harry can also be M2 or M3, we multiply it by 3. Also,
Sally can be F2 so we multiply by 2 as well.
So the total # of elements in event is 24 x 3 x 2 = 144

8.  # of elements in sample space
 (any 3 males, and 2 females)
5 x 4 x 3 x 3 x 2 = 360
 The answer: 144/360

9. Quiz 2.4 #2
 You and two other friends are in the “I love finite” club
with 10 members. The 3 of you are running for the club
committee, which consists of 4 members. If the members
are chosen at random, what is the probability that at least
2 of you will be elected?
A. 21/210
B. 42/210
C. 70/210

10. Quiz 2.4 #2
 You and two other friends are in the “I love finite” club
with 10 members. The 3 of you are running for the club
committee, which consists of 4 members. If the members
are chosen at random, what is the probability that at least
2 of you will be elected?
A. 21/210
B. 42/210
C. 70/210
 Answer: C

11. Summary
 How to find the probability of an event

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