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4 years ago

Ariana's password consists of 1 letter followed by 2 digits. What is the probability of correctly guessing Arabella's password?

Mathematics

1 answer:

AleksandrR [38]4 years ago

3 0

Answer:

1/2600 = 0.00038

Step-by-step explanation:

To find this probability, we first need to find how many ways we can fill each letter and each digit.

The letter has 26 different values, and each digit has 10 different values, so to find the total number of passwords, we just need to multiply the possibilities for each letter and digit:

Total cases = 26 * 10 * 10 = 2600

So the probability of correctly guessing is 1/2600 = 0.00038

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3 years ago

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A survey of 2306 adult Americans aged 18 and older conducted by Harris Interactive found that 417 have donated blood in the past

disa [49]

Answer:

a) p = 0.1808

b) Since 341.54 ≥ 10. Therefore the requirements for constructing a confidence interval for p is satisfied.

c) The interval is (0.1676, 0.194)

d) We are 90% confident that the population proportion of adult Americans who have donated blood in the past two years is between 0.1676 and 0.194

Step-by-step explanation:

Given that:

n = 2306 and x =417

a) Obtain a point estimate for the population proportion (p) is the ratio of sample successes to sample size.

Therefore: p = x / n = 417 / 2306 = 0.1808

p = 0.1808

b) requirements for constructing a confidence interval for p is given by:

np(1-p) ≥ 10

Therefore: np(1-p) = 2306(0.1808)(1 - 0.1808) = 341.54 ≥ 10

Since 341.54 ≥ 10. Therefore the requirements for constructing a confidence interval for p is satisfied.

c) c = 90% = 0.9

α = 1 - 0.9 = 0.1

α / 2 = 0.1 /2 = 0.05

From the probability table, $z_{\frac{\alpha}{2} } = 1.645$

Margin of error (e) = $z_{\frac{\alpha}{2} } \sqrt{\frac{p(1-p)}{n} } =1.645* \sqrt{\frac{0.1808(1-0.1808)}{2306} }=0.0132$

The boundaries are (p - e, p + e) = (0.1808 - 0.0132, 0.1808 + 0.0132) = (0.1676, 0.194)

The interval is (0.1676, 0.194)

d) We are 90% confident that the population proportion of adult Americans who have donated blood in the past two years is between 0.1676 and 0.194

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3 years ago

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The sum of two numbers is 7/8. One addend is 3/4. what is the other? A. 4/4 B. 1/8 C. 1/4 D. 2/8

Dmitrij [34]

Answer:

Step-by-step explanation:

Let the other be $= x$

As the sum of the number is given as $\frac {7}{8}$

And one number is $\frac{3}{4}$

According to question

$\frac{3}{4} +x = \frac{7}{8}$

Subtracting $\frac{3}{4}$ from both sides we get

$\frac{3}{4} +x - \frac{3}{4} = \frac{7}{8} - \frac{3}{4}$

Taking LCM of 4 and 8 we get 8

And making

$\frac{3}{4}$ and $\frac{7}{8}$ like fraction by making denominator same.

Multiply $\frac{3}{4}$ by 2 in numerator and denominator and multiply $\frac {7}{8}$ by 1 in numerator and denominator we get

$x= \frac{7}{8} - \frac{6}{8}$

$x= \frac{7-6}{8}$

$x =\frac{1}{8}$

Hence, the other number is $\frac{1}{8}$

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3 years ago

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