What is 1/3 simplified

Among persons donating blood to a clinic, 85% have Rh+ blood (that is, the Rhesus factor is present in their blood.) Six people

Leona [35]

Answer:

a) There is a 62.29% probability that at least one of the five does not have the Rh factor.

b) There is a 22.36% probability that at most four of the six have Rh+ blood.

c) There need to be at least 8 people to have the probability of obtaining blood from at least six Rh+ donors over 0.95.

Step-by-step explanation:

For each person donating blood, there are only two possible outcomes. Either they have Rh+ blood, or they do not. This means that we use the binomial probability distribution to solve this problem.

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 combinatios 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.

In this problem we have that:

$p = 0.85, n = 6$ .

a) fine the probability that at least one of the five does not have the Rh factor.

Either all six have the factor, or at least one of them do not. The sum of the probabilities of these events is decimal 1. So:

$P(X < 6) + P(X = 6) = 1$

$P(X < 6) = 1 - P(X = 6)$

In which:

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

$P(X = 6) = C_{6,6}.(0.85)^{6}.(0.15)^{0} = 0.3771$

So

$P(X < 6) = 1 - P(X = 6) = 1 - 0.3771 = 0.6229$

There is a 62.29% probability that at least one of the five does not have the Rh factor.

b) find the probability that at most four of the six have Rh+ blood.

Either more than four have Rh+ blood, or at most four have. So

$P(X \leq 4) + P(X > 4) = 1$

$P(X \leq 4) = 1 - P(X > 4)$

In which

$P(X > 4) = P(X = 5) + P(X = 6)$

$P(X = 5) = C_{6,5}.(0.85)^{5}.(0.15)^{1} = 0.3993$

$P(X = 6) = C_{6,6}.(0.85)^{6}.(0.15)^{0} = 0.3771$

$P(X > 4) = P(X = 5) + P(X = 6) = 0.3993 + 0.3771 = 0.7764$

$P(X \leq 4) = 1 - P(X > 4) = 1 - 0.7764 = 0.2236$

There is a 22.36% probability that at most four of the six have Rh+ blood.

c) The clinic needs six Rh+ donors on a certain day. How many people must donate blood to have the probability of obtaining blood from at least six Rh+ donors over 0.95?

With 6 donors:

$P(X = 6) = C_{6,6}.(0.85)^{6}.(0.15)^{0} = 0.3771$

37.71% probability of obtaining blood from at least six Rh+ donors over 0.95.

With 7 donors:

$P(X = 6) = C_{7,6}.(0.85)^{6}.(0.15)^{1} = 0.3960$

0.3771 + 0.3960 = 0.7764 = 77.64% probability of obtaining blood from at least six Rh+ donors over 0.95.

With 8 donors

$P(X = 6) = C_{8,6}.(0.85)^{6}.(0.15)^{2} = 0.2376$

0.3771 + 0.3960 + 0.2376 = 1.01 = 101% probability of obtaining blood from at least six Rh+ donors over 0.95.

There need to be at least 8 people to have the probability of obtaining blood from at least six Rh+ donors over 0.95.

5 0

3 years ago

What is a ajdacent angle

icang [17]

Two angles<span> are </span>Adjacent<span> when they have a common side and a common vertex (corner point) and don't overlap</span>

3 0

3 years ago

I need help trying to find the trig function for this problem

Anon25 [30]

9514 1404 393

Answer:

x ≈ 136.7 ft

Step-by-step explanation:

As you have marked, the relevant sides are the adjacent side and the hypotenuse. The mnemonic SOH CAH TOA reminds you ...

Cos = Adjacent/Hypotenuse

For this triangle, that means ...

cos(43°) = (100 ft)/x

x = (100 ft)/cos(43°) . . . . . . . . . . multiply both sides by x/cos(43°)

x ≈ 136.73 ft

The length x is about 136.7 feet.

5 0

3 years ago

A scientist has two solutions, which she has labeled Solution A and Solution B. Each contains salt. She knows that Solution A is

Yuri [45]

Answer:

x= 44 ounces y = 66 ounces

Step-by-step explanation:

Distribution would be an increase to find 80% salt.

Where we use 4/5 = 80 but use here 4/5.

We find 19/20 but just say 95 for solution B =

Let x = the number of ounces of Solution A

Let y = the number of ounces of Solution B

x + y = 110 y = 110 - x

(70x + 95y) = 4/5 x 110

70x + 95y = 88

70x + 95 y = 88

70x + 95 (88 - x) = 8800 make units equal or for start convert decimalization = same units as 2nd multiplied value.

70x + 8360 - 88x = 8800

-10x - 8360 - 8800 = y

-10x = 440

x = 44 ounces

y = 110- 44

y = 66 ounces

4 0

3 years ago

Read 2 more answers

What is the distance between the points (2, 10) and (-6, 4) on the coordinate plane?

Galina-37 [17]

It's 3/4 because (y2-y1)/(x2-x1)

3 0

4 years ago