Mathematics (HELP)

14) A prime number between 300 and 450 is chosen at random. The table shows the probability that the number lies in different ranges.

Prime number, n Probability
300 ⩽ n < 330 0.16
330 ⩽ n < 360 0.24
360 ⩽ n < 390 x
390 ⩽ n < 420 0.16
420 ⩽ n < 450 0.24

14 (a) Work out the value of x.
[2 marks]



14 (b) Work out the probability that the prime number is greater than 390
[1 mark]


14 (c) There are four prime numbers between 300 and 330
How many prime numbers are there between 300 and 450?
[2 marks]

I don't understand the mark scheme do you guys have another method to work this out?

Remember that the sum of probabilities =1 and that will solve the first part.

The second part is adding together the probabilities of finding prime numbers in certain regions that contain prime numbers greater than 390.

The third part is using that the prime numbers are chosen at random so that each prime number has probability 1/N, where N is the number of prime numbers between 300 and 450.

Thank you but I'm still lost on the third one?

Each prime number has probability 1/N and you are given the number of prime numbers between 300 and 330 and thus you can work out an expression for the probability of finding a prime number between 300 and 330 and then you equate this with the probability of finding a prime number between 300 and 330 given in the table and then solve for N.

14) A prime number between 300 and 450 is chosen at random. The table shows the probability that the number lies in different ranges.

Prime number, n Probability
300 ⩽ n < 330 0.16
330 ⩽ n < 360 0.24
360 ⩽ n < 390 x
390 ⩽ n < 420 0.16
420 ⩽ n < 450 0.24

14 (a) Work out the value of x.
[2 marks]



14 (b) Work out the probability that the prime number is greater than 390
[1 mark]


14 (c) There are four prime numbers between 300 and 330
How many prime numbers are there between 300 and 450?
[2 marks]

I don't understand the mark scheme do you guys have another method to work this out?

Hi there
I've moved your thread to the Maths forum where hopefully you'll get more answers In future, it's best to select the subject from the list here and create a thread in there instead If you want to see where threads belong, check out this thread

Oh, I never knew I should probably start doing that, thank you.