Probability (1) Flashcards
Equation for P(AuB)?
P(AuB) = P(A) + P(B) - P(AnB)
P(AuB) = P(A) + P(B) - P(AnB)
Equation for P(AuB)?
What if A and B are independent variables?
A does not affect the likelihood of B
A does not affect the likelihood of B
What if A and B are independent variables?
Calculate P(AnB) for independent variables?
P(A) * P(B)
P(A) * P(B)
Calculate P(AnB) for independent variables?
What if A and B are mutually exclusive?
When A cannot happen at the same time as B
When A cannot happen at the same time as B
What if A and B are mutually exclusive?
P(AnB) when mutually exclusive?
0
0
P(AnB) when mutually exclusive?
Four cards from a regular pack of 52 playing card. Find probability that all four cards are aces with replacement?
4/52 * 4/52 * 4/52 * 4/52
Four cards from a regular pack of 52 playing card. Find probability that all four cards are aces without replacement?
4/52 * 3/51 * 2/50 * 1/49
“Given that”
Reduces the total number of students
Reduces the total number of students
“Given that”
Formula for P(A|B)
P(AnB) / P(B)
P(AnB) / P(B)
Formula for P(A|B)
Event J and K are independent events, where P(J)=0.7 and P(K)=0.1
Find P(J n K) and P(J u K)
Find P(L | K’)
P(J n K) = 0.7 * 0.1 = 0.07
P(J u K) = 0.7 + 0.1 - 0.07 = 0.73
P(L n K’) / P(K’) = 0.27 / 0.9 = 0.3
Erwin drivers a delivery van for a company that sells fragile glasses. The probability that a glass is delivered on time is 0.8. The probability that a glass is broken but delivered on time is 0.56
Erwin claims that the probability of a glass being broken is not affected by the time he delivers it. If Erwin is correct, what’s the probability of the glass being broken when it’s delivered
Let B = glass broken and T = glass delivered on time
If B and T are independent, then P(B) = P(B|T) = 0.56
Erwin drivers a delivery van for a company that sells fragile glasses. The probability that a glass is delivered on time is 0.8. The probability that a glass is broken but delivered on time is 0.56
Erwin is incorrect, the probability that a sculpture is broken when it’s delivered is 0.5. Find the probability that a sculpture was delivered late, give n it wasn’t broken when it was delivered
Use a tree diagram. Fill in the probabilities and for T’, use algebra
Since P(B | T’) and I want to find P(T’ | B’). Find x as P(B) = 0.5
Now find P(T’ | B’) and P(T’ n B’)/P(B’)
