Explain the level of uncertainties involve in concept of probability. The next generation of miniaturized wireless capsules with active locomotion will require two miniature electric motors to maneuver each capsule. Suppose 10 motors have been fabricated but that, in spite of tests performed on the individual motors, 2 will not operate satisfactorily, when placed into a capsule. To fabricate a new capsule, 2 motors will be randomly selected, find the probability that: (i) Both motors will operate satisfactorily in the capsule. (ii) One motor will operate satisfactorily and the other will not.

a) the probability that Both motors will operate satisfactorily in the capsule 0.6222

b) the probability that One motor will operate satisfactorily and the other will not is 0.3556

Step-by-step explanation:

Given that;

total number of motors N = 10

number of motors will not operate satisfactory m = 2

number of motors randomly selected n = 2

let X be number of motors will that will not operate successfully

here, X≅Hyper geometric (x; N,n,m)

The probability mass function of x is;

P (X = x)=  { m }   {N - m }

                  {x }    {n - x}

        ⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻

                     { N }

                     { n  }

a)

the probability that both motors will operate satisfactorily in the capsule i.e no motor will not operate satisfactory

so

P(X= 0)  = { 2 }    { 10 - 2 }

                 {0 }    { 2 - 0}

        ⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻

                     { 10 }

                     { 2  }

so

P (X = 0)  = { 2 }   { 8}

              {  0 }   { 2  }

        ⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻

                     { 10 }

                     { 2  }

p(P= 0)=1×28 / 45 = 28/45 = 0.6222

Therefore the probability that Both motors will operate satisfactorily in the capsule 0.6222

b)

the probability that one motor will operate satisfactorily and the other will not.

P(X=1)  = { 2 }   { 10 - 2 }

              {  1 }    { 2 - 1  }

        ⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻

                     { 10 }

                     { 2  }

so

P(X=1)  = { 2 }   { 8 }

              {  1 }   { 1  }

        ⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻

                     { 10 }

                     { 2  }

P(X=1)  = 2×8 / 45 = 16/45 = 0.3556

Therefore the probability that One motor will operate satisfactorily and the other will not is 0.3556

15

step-by-step explanation:

we are given the following expression and we are to solve it and find the product:

-13 × (-5)

solving the given expression in the standard order of solving a mathematical expression, beginning with the opening of brackets and then multiplying the terms and changing their signs.

-3 × -5 = 15 (answer is positive because when negative is multiplied with negative, it gives a positive answer)