Two coins are flipped 1,000 times with the following frequencies 2 tails 210 1 tail 480 0 tail 310. Empirical and theoretical probability

Question

Two coins are flipped 1,000 times with the following frequencies  2 tails 210 1 tail 480  0 tail 310. Empirical and theoretical probability

lyrae · Answer

Empirical
2 tail: 210/1000 = 0.21
1 tail: 480/1000 = 0.48
0 tail: 310/1000 = 0.31

Theoretical
2 coins gives four possible outcomes with equal probabillity every time you throw:

       Coin 1      Coin 2      Probabillity
1:    tail           tail           1/4
2:    head        tail           1/4
3:    tail           head        1/4
4:    head        head        1/4

In this particular case, 2 and 3 are the same (1 tail) so their probabillity is added 
1/4 + 1/4 = 2/4 = 1/2

This gives us the final result:
2 tail: 1/4 = 0.25
1 tail: 1/2 = 0.50
0 tail  1/4 = 0.25

anonymous · Answer

Thank you so much!,

anonymous · Answer

a certain dry cereal is packaged on 2 different machines. machine a is set on aveage so that it fills the boxes with 24.5 oz of cereal and standard deviation of 0.4 oz. machine b is set so that it fills the boxes on average with 24 oz of cereal with a standard deviation of 0.2oz. describe which machine is more consistent and why