independent events and how to recognize them

2. Independent Events
Whatever happens in one event has absolutely nothing to do
with what will happen next because:
1. The two events are unrelated
OR
2. You repeat an event with an item whose numbers will not
change (eg.: spinners or dice)
OR
3. You repeat the same activity, but you REPLACE the item that
was removed.
The probability of two independent events, A and B, is equal to the
probability of event A times the probability of event B.
P(A, B) = P(A) P(B) Slide 2

3. Find the probability
• P(jack, factor of 12) 1
5
5
8
x =
5
40
1
8
Slide 3

4. Find the probability
• P(6, not 5)
1
6
5
6
x =
5
36
Slide 4

5. 1
2
1
5
1 1 1
2 5 10
 
S
T
R
O
P1
2
3
6
5
4
Example: Suppose you spin each of these two spinners. What
is the probability of spinning an even number and a vowel?
P(even) = (3 evens out of 6 outcomes)
(1 vowel out of 5 outcomes)P(vowel) =
P(even, vowel) =
Independent Events
Slide 5

6. Examples:
1. Removing (selecting randomly) three red marbles without
replacement from a bag that contains six red and nine blue marbles.
2. Selecting a red card from a deck of cards, returning the card to the
deck, shuffling the card, and selecting a second red card.
3. Rolling two dice.
4. The weather and how likely you are to go visiting. You have decided
that there is a 50% chance that you will visit your friend if it does
not snow, and a 10% chance if it does snow.
DEPENDENT
INDEPENDENT
INDEPENDENT
DEPENDENT