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:
Step-by-step explanation:
(2L)(2W)(3H) = 12LWH.
Amelia gets it.
The sequence is geometric. Any exponential function models geometric growth. Recall the general nth term of a geometric sequence is a*(r)^(n-1) which is very similar to the form y = a*b^x. The big difference is that the x function is continuous while the function in terms of n is discrete. In this case, the common ratio is r = 1.10 to indicate we have 10% growth. Notice how 100%+10% = 1.00+0.10 = 1.10
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The first quadrant is where x and y are both positive. Since x is the time in years, it doesn't make sense to talk about negative years or negative years have passed by. We can have a negative balance in a bank account, so it makes sense to have y be negative. However, Mr Sullivan starts with some positive amount and his account grows every year. So there's no way that y can be negative in this case.
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The point (0,200) is the y intercept. It represents the starting amount he deposited into the account, which was the $200. Keep in mind that no other deposits were made, and he cannot pull money out of the account if he wants his account to grow according to the graph. Also, the interest rate must remain at 10%.
Answer:
190
Step-by-step explanation:
