The probability that a train leaves on time is 0.7. the probability that the train arrives on time and leaves on time is 0.56. what is the probability that the train arrives on time, given that it leaves on time?

 The required probability is 0.8.

Step-by-step explanation:  Let, 'E' denotes the event that a train leaves on time and 'F' denotes the event that the train arrives on time.

Then, according to the given information,

The event that the train arrives on time and leaves on time will be

So,

We are to find the probability that the train arrives on time, given that it leaves on time, ie., P(F/E).

We have

Thus, the required probability is 0.8.

first option

a function is a relation in which an input is paired with exactly one output.

so, let's find the right answer.

in our first option, our inputs are january, february, and march. the outputs are 30, 28, and 25. each input has it's own output. this is correct!

our second option we know is incorrect, because ms. valverade has two outputs, dogs and cats. this is not a function.

our third option is incorrect as well. the yellow square has two ouputs, the square and the triangle.

lastly, in our fourth option, we see the number 7 two times with a different output. therefore, this is not a function.

remember: each input must be paired with only one output!