• Find the probability of a family having five girls in a row and then one boy.
• Then begin on your work for the next few minutes. Page 612 1-57 odd. Check answers in the back.

• In how many ways can a police department arrange eight suspects in a police line up if each contains all five people.

I can find the probability of one event and a second event occurring.
I can compute conditional probabilities.

Independent Events
Two events are independent events if the occurrence of either of them has no effect on the probability of the other.

And Probabilities with Independent
Events
If A and B are independent events, then
P(A and B) = P(A)•P(B)

• A U.S. roulette wheel has 38 numbered slots
(1 – 36, 0, and 00). Of the 38 compartments,
18 black, 18 red, and two are green. A play has the dealer spin the wheel and a small ball in opposite directions. As the ball slows to a stop, it can land with equal probability on any one of the 38 numbered slots. Find the probability of red occurring on two consecutive plays.

The wheel has 38 equally likely outcomes and 18 are red. So, the probability of red occurring on a play is 18/38 or 9/19. The result that occurs on each play is independent of all previous results.
9

9
P(red and red) = P(red)*P(red) = =
19 19
81
361

Find the probability of green occurring on two consecutive plays on a roulette wheel.

A family had nine girls born in a row.
Find the probability of this occurrence.
• The probability of having a baby girl is ½. So, the probability of having nine girls is
P(nine girls) = ½ * ½* ½ * ½* ½ * ½* ½ * ½* ½ =
1
 
1
512
• The probability of having nine girls in a row is
1
512

Find the probability of a family having four boys in a row.

• If the probability that South Florida will be hit by a hurricane in any single year is 5/19. (a)
What is the probability that South Florida will be hit by a hurricane in three consecutive years? (b) What is the probability that South
Florida will NOT be hit by a hurricane in the next ten years?

(a) P(hurricane) * P(hurricane) * P(hurricane) =
5/19 * 5/19 * 5/19 = 125/6859
(b) P( no hurricane) = 1 – P(hurricane)
1 – 5/19 = 14/19 or 0.737
P(no hurricane) * P( no hurricane) * P( no hurricane) ten times =


14
 
19

 
0.047

The Probability of an Event
Happening At Least Once
P(event happening at least once) =
1 – P(event does not happen)

You try
• If the probability that South Florida will be hit by a hurricane in any single year is 5/19,
– A. What is the probability that South Florida will be hit by a hurricane in four consecutive years?
– B. What is the probability that South Florida will NOT be hit by a hurricane in the next four years?
– C. What is the probability that South Florida will be hit by a hurricane at least once in the next four years?

Dependent Events
Two events are dependent events if the occurrence of one of them has an effect on the probability of the other.

And Probabilities with Dependent
Events
If A and B are dependent events, then
P(A and B) = P(A)•P(B given that A has occurred)

• Good News: You won a trip to Madrid and can take two people with you, all expenses paid. Bad News: Ten of your cousins have appeared out of nowhere and are begging you to take them. You write each cousin’s name on a card, place the cards in a hat, and select one name. Then you select a second name without replacing the first card. If three of your ten cousins speak
Spanish, find the probability of selecting two Spanishspeaking cousins.

• P(speaks Spanish) * P(speaks Spanish given that we already selected or who speaks Spanish =
3
10

2
9

6
90

1
15
or 0.067

You try
• You are dealt two cards from a
52-card deck. Find the probability of getting two kings.

• You are dealt three cards from a 52card deck. Find the probability of getting three hearts.

Conditional Probability
The conditional probability of B , given A , written P(B|A), is the probability that event
B occurs computed on the assumption that event A occurs.

• A letter is randomly selected from the letters of the English alphabet. Find the probability of selecting a vowel, given that the outcome is a letter that precedes h.
• P(vowel|letter precedes h) so
Sample Space is {a, b, c, d, e, f, g}
P(vowel | letter precedes h) = 2/7

You try
• You are dealt one card from a 52-card deck.
Find the probability of getting a heart, given that the card you were dealt is a red card.

Applying Conditional Probability to
Real-World Data
P(B|A) = observed number of times B and A occur together observed number of times A occurs

• The table below shows the differences in political ideology per 100 males and per 100 females in the
2000 U.S. presidential election. Assuming that these numbers are representative of all Americans and one American is randomly selected, find the probability that the person
– A. Is liberal, given that the person is female.
– B. Is male, given that the person is conservative.
Liberal Moderate Conservative
Male
Female
16
20
45
55
39
25

• P(liberal given female) = 20/100 = 1/5
• P(male given conservative) = 39/64

You try
• If only one American is randomly selected, find the probability that the person
– a. Is conservative, given that the person is male
– b. Is female, given that the person is liberal
Male
Female
Liberal
16
20
Moderate
45
55
Conservative
39
25

Events Involving And; Conditional
Probability