Probability (1)

Question 1

Equation for P(AuB)?

Answer 1

P(AuB) = P(A) + P(B) - P(AnB)

Question 2

P(AuB) = P(A) + P(B) - P(AnB)

Answer 2

Equation for P(AuB)?

Question 3

What if A and B are independent variables?

Answer 3

A does not affect the likelihood of B

Question 4

A does not affect the likelihood of B

Answer 4

What if A and B are independent variables?

Question 5

Calculate P(AnB) for independent variables?

Answer 5

P(A) * P(B)

Question 6

P(A) * P(B)

Answer 6

Calculate P(AnB) for independent variables?

Question 7

What if A and B are mutually exclusive?

Answer 7

When A cannot happen at the same time as B

Question 8

When A cannot happen at the same time as B

Answer 8

What if A and B are mutually exclusive?

Question 9

P(AnB) when mutually exclusive?

Answer 9

0

Question 10

0

Answer 10

P(AnB) when mutually exclusive?

Question 11

Four cards from a regular pack of 52 playing card. Find probability that all four cards are aces with replacement?

Answer 11

4/52 * 4/52 * 4/52 * 4/52

Question 12

Four cards from a regular pack of 52 playing card. Find probability that all four cards are aces without replacement?

Answer 12

4/52 * 3/51 * 2/50 * 1/49

Question 13

“Given that”

Answer 13

Reduces the total number of students

Question 14

Reduces the total number of students

Answer 14

“Given that”

Question 15

Formula for P(A|B)

Answer 15

P(AnB) / P(B)

Question 16

P(AnB) / P(B)

Answer 16

Formula for P(A|B)

Question 17

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’)

Answer 17

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

Question 18

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

Answer 18

Let B = glass broken and T = glass delivered on time

If B and T are independent, then P(B) = P(B|T) = 0.56

Question 19

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

Answer 19

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’)