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Assume that there are an equal number of births in each month so that the probability is that a person chosen at random was born

NikAS [45]

Answer:

0.2773 = 27.73% probability that at the May celebration, exactly two members of the group have May birthdays

Step-by-step explanation:

For each person, there are only two possible outcomes. Either they have a birthday in May, or they do not. The probability of a person having a birthday in May is independent of any other person. This means that the binomial probability distribution is used to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

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

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

And p is the probability of X happening.

Probability of a person being in May:

May has 31 days in a year of 365. So

$p = \frac{31}{365} = 0.0849$

Group of 20 friends:

This means that $n = 20$

What is the probability that at the May celebration, exactly two members of the group have May birthdays?

This is P(X = 2).

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 2) = C_{20,2}.(0.0849)^{2}.(0.9151)^{18} = 0.2773$

0.2773 = 27.73% probability that at the May celebration, exactly two members of the group have May birthdays

3 0

3 years ago

PLZ HELP

Mashutka [201]

(5-5) x
It is different because when you distribute the x it will make it 5x-5x while all the other equations are 5-5x

7 0

3 years ago

Show that the sum of two concave functions is concave. Is the product of two concave functions also concave?

spayn [35]

Answer with explanation:

Let us assume that the 2 functions are:

1) f(x)

2) g(x)

Now by definition of concave function we have the first derivative of the function should be strictly decreasing thus for the above 2 function we conclude that

$\frac{d}{dx}\cdot f(x)$

Now the sum of the 2 functions is shown below

$y=f(x)+g(x)$

Diffrentiating both sides with respect to 'x' we get

$\frac{dy}{dx}=\frac{d}{dx}\cdot f(x)+\frac{d}{dx}\cdot g(x)\\\\$

Since each term in the right of the above equation is negative thus we conclude that their sum is also negative thus

$\frac{dy}{dx}$

Thus the sum of the 2 functions is also a concave function.

Part 2)

The product of the 2 functions is shown below

$h=f(x)\cdot g(x)$

Diffrentiating both sides with respect to 'x' we get

$h'=\frac{d}{dx}\cdot (f(x)\cdot g(x))\\\\h'=g(x)f'(x)+f(x)g'(x)$

Now we can see the sign of the terms on the right hand side depend on the signs of the function's themselves hence we remain inconclusive about the sign of the product as a whole. Thus the product can be concave or convex.

8 0

3 years ago

2. Find the compound interest on Rs.25, 000 after 2 years compounded

Allushta [10]

Answer:25,000 in 2 years at annual compound interest, if the rates for the successive years be 4% and 5% per annum respectively is: (1) Rs. 30,000 (2) Rs. 26,800 fa) Rs.

A=P[1+

100

r

]

n

⇒ A=Rs.25,000×(

100

106

)

3

⇒ 25,000×

50

53

×

50

53

×

50

53

⇒ A=Rs.29,775.40

⇒ CI=A−P

⇒ Rs.29,775.40−Rs.25,000

∴ CompoundInterest=Rs.4775.40.

6 0

3 years ago

Can someone help me fully simplify this step by step pleaseeeee

JulijaS [17]

$2x - 7x + 2 + 1 - 2$

$2x - 7x + 3 - 2$

$- 5x + 1$

7 0

2 years ago

Helpppp plssss brainliest if you anwser fast