What is the probability that in a class of 20 students, 2 of them will have the same birthday?

If we sample from a small finite population without replacement, the binomial distribution should not be used because the event

seropon [69]

Answer:

5/4324 = 0.001156337

Step-by-step explanation:

To better understand the hyper-geometric distribution consider the following example:

There are 100 senators in the US Congress, and suppose 60 of them are republicans so 100 - 60 = 40 are democrats).

We extract a random sample of 30 senators and we want to answer this question:

What is the probability that 10 senators in the sample are republicans (and of course, 30 - 10 = 20 democrats)?

The answer using the h-g distribution is:

$\large \frac{\binom{60}{10}\binom{100-60}{30-10}}{\binom{100}{30}}=\frac{\binom{60}{10}\binom{40}{20}}{\binom{100}{30}}$

Now, imagine there are 56 senators (56 lottery numbers), 6 are republicans (6 winning numbers and 50 losers), we extract a sample of 6 senators (the bettor selects 6 numbers). What is the probability that 4 senators are republicans? (What is the probability that 4 numbers are winners?).

<em>As we see, the situation is exactly the same,</em> but changing the numbers. So the answer would be

$\large \frac{\binom{6}{4}\binom{56-6}{6-4}}{\binom{56}{6}}=\frac{\binom{6}{4}\binom{50}{2}}{\binom{56}{6}}$

Now compute each combination separately:

$\large \binom{6}{4}=\frac{6!}{4!2!}=15\\\\\binom{50}{2}=\frac{50!}{2!48!}=1225\\\\\binom{50}{6}=\frac{50!}{6!44!}=15890700$

and now replace the values:

$\large \frac{\binom{6}{4}\binom{50}{2}}{\binom{56}{6}}=\frac{15*1225}{15890700}=\frac{18375}{15890700}=\frac{5}{4324}$

and that is it.

If the decimal expression is preferred then divide the fractions to get 0.001156337

6 0

3 years ago

Based on the circle graph how many pounds of milk and eggs does the average American consume each year PLS EXPLAIN FOR BRAINLEST

Gnoma [55]

Answer:

H. 552

Step-by-step explanation:

Circle graph information:

Milk and eggs = x%
Fruits and vegetables = 38%
Cereals = 10%
Meat and fish = 10%
Sugar = 8%
Fats and oils = 4%

Total consumption = 1840 pounds per person

First, calculate the percentage of milk and eggs (the value of x).

Total percentages = 100%

⇒ x + 38 + 10 + 10 + 8 + 4 = 100

⇒ x + 70 = 100

⇒ x = 30

Therefore, 30% of food consumption is milk and eggs.

To calculate the number of pounds of milk and eggs the average American consumes each year, simply find 30% of the total consumption:

= 30% of 1840

= 30% × 1840

$=\sf \dfrac{30}{100} \times 1840$

= 552

Therefore, the average American consumes 552 pounds of milk and eggs each year.

5 0

2 years ago

Read 2 more answers

Rewrite the expressions in each pair so that they have the same base. c) (1 /2)^2x and (1/ 4)^x - 1

just olya [345]

I'm not completely sure but this is what I would do.
evaluate <span>(1/ 4)^x - 1 </span>as is. But change the (1 /2)^2x to (2/4)^2x. This way both fractions have the same denominator and in this sense, the same base. The 2/4 base still evaluates into 1/2 so nothing, mathematically, is being broken here.

7 0

4 years ago

If a woman takes an early pregnancy test, she will either test positive, meaning that the test says she is pregnant, or test neg

k0ka [10]

Answer:

0.0098

Step-by-step explanation:

Probability of being pregnant:100/1000

=1/10.

98% chance:=98/100 ×1/10

=98/1000

Therefore the probability that she really is pregnant is: 0.098

3 0

3 years ago

What is the relationship between the lines with the following equations? 2x+8y=16 y=4x+7

dimulka [17.4K]

They are perpendicular because when you change 2x+8y=16 to slope intercept form it becomes y= -1/4x+2 and the slope (-1/4) is the negative reciprocal of 4, which is the slope for your other equation.

Please comment if you have any questions :)

6 0

3 years ago