Probability Trees Flashcards
What is a probability tree?
A diagram to visualize the probabilities of consecutive events
How do you find the probability of consecutive events happening across a probability tree?
Multiply across the branches
What is the value of B?
0.6
Explanation:
Each branch should sum to 1.
1-0.4=0.6
How many total possible outcomes are there?
4
Explanation:
Each end branch represents a possible outcome. This tree has 4 end branches…
1) Bob catch, Bill catch
2) Bob catch, Bill doesn’t catch
3) Bob doesn’t catch, Bill catch
4) Bob doesn’t catch, Bill doesn’t catch
What is the probability both Bob and Bill catch?
0.63
Explanation:
Multiply across the branches.
P (C, C) = (0.9)*(0.7)=0.63
What is the probability of pulling green both times?
16/49
Explanation:
Multiply across the branches.
P(G,G) = (4/7)*(4/7)=16/49
What is the probability of pulling green on the second try?
4/7
Explanation:
We want the probability that we pulled YG or GG (because either way G was second).
P(Y,G)=( 3/7 )( 4/7)= 12/49
P(G,G)= ( 4/7 )( 4/7)= 16/49
Therefore, the total probability that G was second is..
12/49+16/49= 28/49=4/7
What is the probability it was sunny on Saturday and rainy on Sunday?
0.1
Explanation:
Multiply across the branches.
P(sunny, rainy) =
(0.2)*(0.5)=0.1
What is the probability Bob does not catch?
0.1
Explanation:
Each branch should sum to 1.
1-0.9=0.1
What is the probability of picking two of the same color button?
25/49
Explanation:
We want the probability that we pulled YY or GG (because either way the same color was selected twice).
P(Y,Y)=( 3/7 )( 3/7)= 9/49
P(G,G)= ( 4/7 )( 4/7)= 16/49
Therefore, the total probability that the same color was drawn twice is..
9/49+16/49= 25/49
How does “without replacement” impact a probability tree?
When you do not replace what was removed from a bag, the number of that item and the total are both decreased by one for the second draw.
Example:
Given a red marble was drawn first, without replacement, what is the probability that a blue marble is drawn second?
7/9
Explanation:
Since a red marble was drawn first, there is one less in the total; therefore, the denominator of the fraction goes from 10 to 9. The numerator is still 7 because there are still 7 blue marbles.
What is the conditional probability formula? (“Find the probability of A given B”)
The probability of A given B is equal to the probability of A and B divided by the probability of B.
What is the key when you see a question with the word “given”?
Divide by what’s given
What is the probability that a pitch was a fast ball, given it was a strike?
Answer:
0.875
Explanation:
1) Find the probability that the pitch was a fast ball and a strike.
0.42
2) Find the probability of a strike.
0.42+0.06=0.48
3) Divide the probability of the pitch being a fastball and a strike by the probability of a strike.
0.42/0.48= 0.875
What is the probability that a pitch was a strike, given that it was a knuckle ball?
Answer:
0.2
Explanation:
1) Find the probability that the pitch was a strike and a knuckle ball.
0.06
2) Find the probability of a knuckle ball.
0.06 + 0.24=0.3
3) Divide the probability of the pitch being a strike and a knuckle ball by the probability of a knuckle ball.
0.06/0.3= 0.2
Note: This one could also be solved with the shortcut of looking at the strike branch of the knuckleball scenario.
