The yellow pins show as 85% of the total number of pins that Collin ordered
This problem can be solved from first principles, case by case. However, it can be solved systematically using the hypergeometric distribution, based on the characteristics of the problem:
- known number of defective and non-defective items.
- no replacement
- known number of items selected.
Let
a=number of defective items selected
A=total number of defective items
b=number of non-defective items selected
B=total number of non-defective items
Then
P(a,b)=C(A,a)C(B,b)/C(A+B,a+b)
where
C(n,r)=combination of r items selected from n,
A+B=total number of items
a+b=number of items selected
Given:
A=2
B=3
a+b=3
PMF:
P(0,3)=C(2,0)C(3,3)/C(5,3)=1*1/10=1/10
P(1,2)=C(2,1)C(3,2)/C(5,3)=2*3/10=6/10
P(2,0)=C(2,2)C(3,1)/C(5,3)=1*3/10=3/10
Check: (1+6+3)/10=1 ok
note: there are only two defectives, so the possible values of x are {0,1,2}
Therefore the
PMF:
{(0, 0.1),(1, 0.6),(2, 0.3)}
Answer:
(2,0)
Step-by-step explanation:
On the x-axis, the point is at 2. The point has a y-value of 0, as it's on the x-axis.
Answer:
The likelihood that a point chosen inside the square will also be inside the circle: 78.54%
Step-by-step explanation:
- Let x is the side of the suqare
=> the area of the square is: 
- Let d is the diameter of the circle
=> the area of the circle : 
π
However, d=x because of the square property
<=> the area of the circle : 
π
The likelihood that a point chosen inside the square will also be inside the circle:
the area of the circle / the area of the square
= π /
= 
π *100%
= 0.7854 * 100%
= 78.54%
