You are getting a line-up ready for a school kickball game. you have 77 girls and 77 boys. the rules state each child must kick
1 answer:
1. Since each child kicks the same number of times, it is not important whether he or she kicks 1 time, 2, 3 or more times. So let all of them kick 1 time.
2. assume we start with a girl. We can start with either of the 77 girls, then second is a boy which can be either of the 76, the third is a girl which can be either of the 76 remaining, then the forth is one of the 76 boys...
3. So starting with a girl we have
77*(77)*76*(76)*75*(75)....*2*(2)*1*(1)=77!*77!
4. OR we could have started with a boy, where we would get again 77!*77!
5. Answer: 77!*77!+77!*77!=2
2. assume we start with a girl. We can start with either of the 77 girls, then second is a boy which can be either of the 76, the third is a girl which can be either of the 76 remaining, then the forth is one of the 76 boys...
3. So starting with a girl we have
77*(77)*76*(76)*75*(75)....*2*(2)*1*(1)=77!*77!
4. OR we could have started with a boy, where we would get again 77!*77!
5. Answer: 77!*77!+77!*77!=2
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Answer:
a) 0.2741 = 27.41% probability that at least 13 believe global warming is occurring
b) 0.7611 = 76.11% probability that at least 110 believe global warming is occurring
Step-by-step explanation:
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
In which is the number of different combinations of x objects from a set of n elements, given by the following formula.
And p is the probability of X happening.
The expected value of the binomial distribution is:
The standard deviation of the binomial distribution is:
Normal probability distribution
Problems of normally distributed samples can be solved using the z-score formula.
In a set with mean and standard deviation
, the zscore of a measure X is given by:
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
When we are approximating a binomial distribution to a normal one, we have that ,
.
In this problem, we have that:
(a) For a sample of 16 Americans, what is the probability that at least 13 believe global warming is occurring?
Here , we want
. So
In which
0.2741 = 27.41% probability that at least 13 believe global warming is occurring
(b) For a sample of 160 Americans, what is the probability that at least 110 believe global warming is occurring?
Now . So
Using continuity correction, this is , which is 1 subtracted by the pvalue of Z when X = 109.5. So
has a pvalue of 0.2389
1 - 0.2389 = 0.7611
0.7611 = 76.11% probability that at least 110 believe global warming is occurring
Hey there :)
- tan²x + sec²x = 1 or 1 + tan²x = sec²x
sin²x + cos²x = 1
Divide the whole by cos²x
so 
and
so 
Therefore,
tan²x + 1 = sec²x
Take tan²x to the other side {You will have the same answer}
1 = - tan²x = sec²x or sec²x - tanx = 1
- tan²x + sec²x = 1 or 1 + tan²x = sec²x
sin²x + cos²x = 1
Divide the whole by cos²x
and
Therefore,
tan²x + 1 = sec²x
Take tan²x to the other side {You will have the same answer}
1 = - tan²x = sec²x or sec²x - tanx = 1