Aand b are independent events p(a) = .50 p(b)=.20 what is p(a/b)

P(a|b) = 1/2

Step-by-step explanation:

* Lets study the meaning independent probability  

- Two events are independent if the result of the second event is not

  affected by the result of the first event

- If A and B are independent events, the probability of both events  

is the product of the probabilities of the both events

- P (A and B) = P(A) · P(B)  ⇒ P (A ∩ B) = P(A) · P(B)

- If A and B are two events, then the conditional probability of A

 given B is defined as P(A|B) = P(A∩B)/P(B)

* Lets solve the problem

∵ P(a) = 0.50

∵ P(b) = 0.20

∵ a and b are independent events

∴ P (a ∩ b) = P(a) · P(b)

∴ P (a ∩ b) = 0.50 × 0.20 = 0.10

∵ P(a|b) = P(a∩b)/P(b)

∴ P(a|b) = 0.10/0.20 = 1/2

* P(a|b) = 1/2

54 kilometers per hour

step-by-step explanation:

according to rules:

1 km = 1000 meter

which means that 1 meter = 1/1000 km

1 hour = 3600 second [ as 1 hour = 60 min = 60 *60 seconds ]

which means that 1 second = 1/3600 hour

therefore, 1 kilometer/hour =

thus to convert 15 meter per second to kilometer per hour, we multiply 15 to 3.6 kilometer/hour.

15 meter/second=   which is the required answer.

- "runner b is moving at a slower rate."

- "the graphs shown are graphs of distance(km) against time(min).

the slopes of this graphs are are given by:

slope = (change in y)/(change in x)

= (change in distance)/(change in time)

this is the formula for finding the speed. so, the slope of these graphs represent the speed of the runner.

taking each division in the graph to represent 1 on both axis:

runner a ⇒ speed = (2-0)/(1-0)

= 2/1

= 2 km/min

runner b ⇒ speed = (3-0)/(3-0)

= 3/3

= 1 km/min

this shows that   runner b is moving at a slower rate."