What is the length of each side of a square if it’s area is 361ft2?
1 answer:
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Answer:
103, 776
Step-by-step explanation:
There are 48 possibilities, and you are picking 3.
Now, the order does matter (aka, if the same 3 athletes won but got different places, we would still consider it to be a separate possibility)
(this is considered "without repetitions")
the number of permutations (arrangement combinations where the order does matter) without repetitions formula:
Number of permutations
without <em>repetitions </em>= nPr
=
(
[the P is for combinations [where the order does matter, if the order didn't matter then it would be C, and it would be a different formula.]
n is the total number of objects.
r is the number of objects selected]
<em>(a repetition would be like two versions of the same person competing, which doesn't make sense)</em>
{the ! means factorial:
5! = 5 x 4 x 3 x 2 x 1}
{for example, if there are 5 people to give a presentation, and they can go in any order [but cannot repeat their presentation], so they all must fill 5 slots}
{for the first slot there are 5 choices, the second slot there are 4 choices...}
)
So, if we follow this formula:
n: 48
r: 3
=
=
(the 45! cancel out)
= 48 * 47 * 46
= 103, 776
(or, without the formula:
for the first choice (lets say of gold), there are 48 options
for the second choice (lets say silver), there are 47 options left to choose from
for the third choice (lets say bronze), there are 46 options left to choose from
)
Answer:
a) The probability that this whole shipment will be accepted is 30%.
b) Many of the shipments with this rate of defective aspirin tablets will be rejected.
Step-by-step explanation:
We have a shipment of 3000 aspirin tablets, with a 5% rate of defects.
We select a sample of size 48 and test for defectives.
If more than one aspirin is defective, the batch is rejected.
The amount of defective aspirin tablets X can be modeled as a binomial distribution random variable, with p=0.55 and n=48
We have to calculate the probabilities that X is equal or less than 1: P(X≤1).