Answer:
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
