Aset of cards contains cards numbered 1 – 8. mrs. jacob’s class is conducting an experiment in which a card is drawn from the pile, the number is recorded, and then the card is returned to the set. the class will conduct 1,000 trials. based on the theoretical probability, which is the best prediction for the number of times a 4 will be drawn from the pile? 111 125 143 250

2nd Option is correct.

Step-by-step explanation:

We are given a set of cards containing numbers from 1 to 8 on each cards.

Randomly a card is drawn and noted.

This is repeated 1000 times.

To find: Number of time 4 will be drawn from the pack using theoretical probability.

We know that,

Theoretical Probability: Probability which is based on reasoning  and written as a ratio of the number of favorable outcomes to the total number of outcomes.

Probability of getting 4 from the pack =

Now, Number of the times 4 will be drawn from pack out of 1000 times

=

= 125

Therefore, 2nd Option is correct.

i think it's eleven too, don't woosh me here, but according to the "experts" it's 2.

the proof starts from the peano postulates, which define the natural

numbers n. n is the smallest set satisfying these postulates:

  p1.   1 is in n.

  p2.   if x is in n, then its "successor" x' is in n.

  p3.   there is no x such that x' = 1.

  p4.   if x isn't 1, then there is a y in n such that y' = x.

  p5.   if s is a subset of n, 1 is in s, and the implication

      (x in s => x' in s) holds, then s = n.

then you have to define addition recursively:

  def: let a and b be in n. if b = 1, then define a + b = a'

      (using p1 and p2). if b isn't 1, then let c' = b, with c in n

      (using p4), and define a + b = (a + c)'.

then you have to define 2:

  def:   2 = 1'

2 is in n by p1, p2, and the definition of 2.

theorem:   1 + 1 = 2

proof: use the first part of the definition of + with a = b = 1.

      then 1 + 1 = 1' = 2   q.e.d.

note: there is an alternate formulation of the peano postulates which

replaces 1 with 0 in p1, p3, p4, and p5. then you have to change the

definition of addition to this:

  def: let a and b be in n. if b = 0, then define a + b = a.

      if b isn't 0, then let c' = b, with c in n, and define

      a + b = (a + c)'.

you also have to define 1 = 0', and 2 = 1'. then the proof of the

theorem above is a little different:

proof: use the second part of the definition of + first:

      1 + 1 = (1 + 0)'

      now use the first part of the definition of + on the sum in

      parentheses:   1 + 1 = (1)' = 1' = 2   q.e.d.

b and c are the correct answers.

good luck on the quiz! : d