Transcript Probability of Dependent Events

Probability of Dependent Events
Section 10.3
What key words tell us it is a
dependent event?
Vocabulary
• Dependent event - two events whose
occurrence of one event DOES affect the
likelihood that the other event will occur
• Examples:
– A deck of cards
– Drawling a marble, without replacing it, then
drawling another marble
– Your teacher chooses one student to lead a group,
and then chooses another student to lead another
group
Things to Know
Finding the Probability of Two
Dependent Events
Step 1:
Find the probability of A = P(A)
Step 2:
Find the probability of B after A has occurred = P(B after
A)
Step 3:
Multiply the probability of A by the probability of B after
A has occurred = P(A) x P(B after A)
Step 4:
Simplify your fraction
Example 1
Tell whether the events are independent or
dependent. Explain.
1. You flip heads on one coin and tails on another coin.
2. Your teacher chooses one student to lead a group,
and then chooses another student to lead another
group.
3. You choose a marble from a bag and set it aside.
Then you choose another marble from the bag.
4. You choose a marble from a bag, record its color,
and place it back into the bag. Then you choose
another marble from the bag.
Your Turn
Tell whether the events are independent or
dependent. Explain.
1. You choose a blue marble from a bag and set
it aside. Then you choose a green marble
from the bag.
2. You roll a 5 on a number cube and spin blue
on a spinner.
Example 2
You have four $20 bills and three $10 bills.
You randomly choose a bill from your wallet to
pay for lunch. You need more money, so you
choose another bill. What is the probability
that you choose a $20 bill, then a $10 bill?
Your Turn
• You have four $20 bills and three $10 bills. You
randomly choose a bill from your wallet to pay
for lunch. You need more money, so you
choose another bill.
• What is the probability that both bills are $20
bills?
• What is the probability that both bills are $10
bills?
Example 3
You are guessing at two questions on a
multiple choice test. Each question has three
choices: A, B, and C.
1. What is the probability that you guess the correct
answers to both questions?
2. Suppose you can eliminate one of the choices for
each question. How does this change the
probability that your guesses are correct?
Your Turn
• You randomly choose two fish from the bowl.
What is the probability that the first is gold
and without replacing it, the second is red?
Assignment
• What type of events/situations tell us it is a
dependent event? What type of
events/situations tell us it is a independent
event?
• 1 – Easy Breezy, I got this
• 2 – I could use a little more practice
• 3 – I’m totally lost