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Levart [38]
3 years ago
11

If a person picks a pair of different Months, what is the probability that both months (different) have less than 31 days?

Mathematics
1 answer:
wlad13 [49]3 years ago
5 0

Answer:

15.15% probability that both months (different) have less than 31 days.

Step-by-step explanation:

A probability is the number of desired outcomes divided by the number of total outcomes.

Also, the order of the months is not important. For example, picking July and August is the same as picking August and July. So the combinations formula is used to solve this problem

Combinations formula:

C_{n,x} is the number of different combinations of x objects from a set of n elements, given by the following formula.

C_{n,x} = \frac{n!}{x!(n-x)!}

There are 12 months, of which February, April, June, September and November, that is, 5 of them, have less than 31 months.

Desired outcomes:

Picking 2 months from a set of 5(those with less than 31 days). So

D = C_{5,2} = \frac{5!}{2!(3)!} = 10

Total outcomes:

Picking 2 months from a set of 12(all the months). So

T = C_{12,2} = \frac{12!}{2!(10)!} = 66

Probability:

P = \frac{10}{66} = 0.1515

15.15% probability that both months (different) have less than 31 days.

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5 0
3 years ago
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Igoryamba
A and C are the answer
4 0
3 years ago
Read 2 more answers
A researcher is interested in estimating the difference in two population proportions. A sample of 400 from each population resu
sergey [27]

Answer: (-0.086, 0.026)

Step-by-step explanation:

The confidence interval for the difference of two population proportion is given by :-

p_1-p_2\pm\ z_{\alpha/2}\sqrt{\dfrac{p_1(1-p_1)}{n_1}+\dfrac{p_2(1-p_2)}{n_2}}

Given : Significance level : \alpha: 1-0.90=0.10

Critical value : z_{\alpha/2}=1.645

Sample size : n_1=400,\ n_2=400

p_1=0.61,\ p_2=0.64

The 90% confidence interval for the difference in the population proportions will be :-

0.61-0.64\pm\ (1.645)\sqrt{\dfrac{0.61(1-0.61)}{400}+\dfrac{0.64(1-0.64)}{400}}\\\\\approx-0.03\pm0.056=(-0.03-0.056,-0.03+0.056)\\\\=(-0.086, 0.026)

7 0
3 years ago
Plz Help???
GREYUIT [131]
1.
12 liters of 26% acid solution contain 26\% \times 12=0.26 \times 12=3.12 liters of acid.
x liters of 40% acid solution contain 40\%x=0.4x liters of acid.
The third solution is made from the two mixed solution so its volume is 12+x, and the volume of acid in it is 0.4x+3.12. Its concentration is 33% or 0.33.
The concentration of a solution is the volume of the solution divide by the volume of acid in it.

\frac{0.4x+3.12}{12+x}=0.33 \\ 0.4x+3.12=0.33(12+x) \\ 0.4x+3.12=3.96+0.33x \\
0.07x=0.84 \\
x=12

The answer is B.

2.
12 liters of 16% acid solution contain 16\% \times 12=0.16 \times 12=1.92 liters of acid.
x liters of 40% acid solution contain 40\%x=0.4x liters of acid.
The volume of the third solution is 12+x, and the volume of acid in it is 0.4x+1.92. Its concentration is 32% or 0.32.

\frac{0.4x+1.92}{12+x}=0.32 \\
0.4x+1.92=0.32(12+x) \\
0.4x+1.92=3.84+0.32x \\
0.08x=1.92 \\
x=24

The answer is B.

3.
16 liters of 18% acidsolution contain 18\% \times 16=0.18 \times 16=2.88 liters of acid.
x liters of 27% acid solution contain 27\%x=0.27x liters of acid.
The volume of the third solution is 16+x, and the volume of acid in it is 0.27x+2.88. Its concentration is 21% or 0.21.

\frac{0.27x+2.88}{16+x}=0.21 \\
0.27x+2.88=0.21(16+x) \\
0.27x+2.88=3.36+0.21x \\
0.06x=0.48 \\
x=8

The answer is A.

5 0
4 years ago
Which is more likely?
Marina86 [1]

Answer:

Rolling a dice and landing on a number 1-4

Step-by-step explanation:

Flipping a coin is 50% (well like 51 or something but for this they probably mean 50)

Roiling a dice and landing on a number that is 1,2,3, or 4 is 2/3 which is more than 1/2.

8 0
3 years ago
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