Question

3 rotten apples are mixed with 7 good apples in a box. three apples are chosen simultaneously from the box. find probability distribution of number of good apples. find its mean and variance.

Answer 1

Answer:

answer is correct question is wrong

Answer 2

Answer:

mean=2.1

variance=0.63

Step-by-step explanation:

This is an experiment with only two possible outcomes ie: picking a good apple (success) and picking a bad apple (failure).

The probability of success p is $\frac{7}{10} =0.7$

which implies that the probability of failure is $\frac{3}{10}=0.3$

Let $X$ be the number of good apples picked (successes). This becomes our random variable.

In one choosing, the probability distribution becomes

$P(X=x)= p^{x}*(1-p)^{1-x}, x=1,0$

$P(X=x)=0.7^{x}*0.3^{1-x},x=0,1$

Now, when 3 apples are chosen simultaneously from the box, this becomes a binomial distribution with n=3 and p=0.7.

Therefore

$P(X=x)=\left \ ( {{n} \atop {x}} \right)*p^{x}*(1-p)^{n-x}\\P(X=x)=\left \ ( {{3} \atop {x}} \right)*0.7^{x}*0.3^{3-x}, x=0,1,2,3$

The mean of a binomial(n,p) distribution is given as

$mean=np\\mean=3*0.7\\mean=2.1$\\

Its variance is obtained as

$variance=n*p*q\\variance=3*0.7*0.3\\variance=0.63$