Question

40% of a company staff are females. What is the probability that a set of 7 records of the employees
taken at random from the cupboard has 2 records of female staff?​

Answer 1

Step-by-step explanation:

60% are male. so 5 records have male.

Answer 2

Probability that 2 records of female staff out of a set of 7 records of the employees is 0.26 .

Step-by-step explanation:

Given: A company 40% staff are females.

To Find: Probability that 2 records of female staff out of  a set of 7 records of the employees .

Formula  Used:

Bernoulli  distribution is given by:

P(X=k)=nCk $p^{k} q^{n-k}$         ----------------------------- formula no.01

Here,   P(X=k) = The probability of  getting k  records of female staff   out of  number of  n  records of the employees .

n = number records of the employees .

X= A  random variable which takes value of k

 k = number  of  getting  records of female staff  

 p = probability of  getting  one female staff

 q = probability of not getting   one female staff

  As given A company 40% staff  are females.          

   p = probability of getting  one female staff out of 100

          = 40/100 = 2/5

   q= probability of not getting  one female staff.

   q= 1-p

      =1-2/5 =3/5

       n = 7    and  k=2

  Putting the value of n ,p, q and k in formula no.01.

      P(X=2)=7C2 $(\frac{2}{5} )^{2} (\frac{3}{5} )^{5}$

                 $= \frac{7!}{(7-2)! 2!} (\frac{2}{5} )^{2} (\frac{3}{5} )^{5}$

                 $= \frac{7.6.5! }{5! 2!} (\frac{2}{5} )^{2} (\frac{3}{5} )^{5}$

                 $= \ (21) (\frac{2}{5} )^{2} (\frac{3}{5} )^{5}$

                 $= 0.26$

   Thus, probability that 2 records of female staff from a set of 7 records of the employees is 0.26 .