# 7 - Independent & Dependent Events ```P.O.D. #7
basic
In how many ways can a president, vice
president, and secretary be randomly
selected from a class of 25 students?
Pres.
VP
Sec.
Total
25 &times; 24 &times; 23 = 13,000
A garage door code has 5 digits. If no digit
is repeated, how many codes are possible?
1st
2nd
3rd
4th
5th
10 &times; 9 &times; 8 &times; 7 &times; 6
= 30,240
Independent &amp; Dependent Events
Independent events are two or more events in which the
outcome of one event does not affect the outcome of the
other event(s).
Example:
You roll a number cube twice.
Dependent events are two or more events in which the
outcome of one event affects the outcome of the other
event(s).
Example:
You pick one card from a deck of playing cards,
do not replace it, then pick another card.
The probability of two independent events can be found
by multiplying the probability of the first event by the
probability of the second events.
P(A  B) = P(A)  P(B)
Example:
A game requires players to roll two number cubes to move the game
pieces. What is the probability of rolling a 3 or 4 on the first number
cube and then rolling a 5 on the second?
2
1
P(3 or 4) = =
6
3
1
P(5) =
6
1 1
1
P( 3 or 4 AND 5) =
=

3 6
18
The probability of two dependent events can be found
by multiplying the probability of the first event by the
probability of the second event after the first occurs.
P(A  B) = P(A)  P(B following A)
Example:
What is the probability of picking a red card from a deck of
playing cards, not returning it, and then picking a second
red card?
26
1
P(first card is red) =
=
52
2
25
P(second card is red) =
51
1 25
25
P(two red) =
=

2 51
102
Whiteboard:
A carnival game wheel has 12 equal sections. One of the
sections contains a star. To win a prize, players must land
on the section with the star on two consecutive spins.
What is the probability of a player winning?
P(1st
1
star) =
12
P(2nd
1
star) =
12
1 1
1
P(two stars) =
=

12 12
144
Whiteboard:
There are 4 oranges, 7 bananas, and 5 apples in a fruit
basket. Dymond selects a piece of fruit at random. Then
Yair selects a piece of fruit at random. Find the probability
that two apples are chosen.
5
P(first piece is an apple) =
16
4
P(second piece is an apple) =
15
5
4
20
1
P(two apples) =
=
=

16
15
240
12
```