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3 years ago

Find the union of A = {2,3,4} and B = {3,4,5)

Mathematics

1 answer:

DENIUS [597]3 years ago

5 0

Answer:

A U B = {2,3,4, 5}

Step-by-step explanation:

Union means join together

A U B = {2,3,4, 5}

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3 years ago

Suppose you add two vectors A and B . What relative direction between them produces the resultant with the greatest magnitude? W

Anna71 [15]

Answer: The resultant would be the sum and the difference between the vectors.

Step by step explanation: 1. The possible resultant is between the sum of the 2 vectors and the difference between the two vectors.

2. The greatest magnitude is when the vectors lie in the same direction and the sum would be the scalar sum of the two vectors. The angle between the two would be zero degree.

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3 years ago

Q and r are independent events. if p(q) = 1/4 and p(r)=1/5, find p(q and r)

klasskru [66]

Answer:

(b) $\frac{7}{30}$

Step-by-step explanation:

When two p and q events are independent then, by definition:

P (p and q) = P (p) * P (q)

Then, if q and r are independent events then:

P(q and r) = P(q)*P(r) = 1/4*1/5

P(q and r) = 1/20

P(q and r) = 0.05

In the question that is shown in the attached image, we have two separate urns. The amount of white balls that we take in the first urn does not affect the amount of white balls we could get in the second urn. This means that both events are independent.

In the first ballot box there are 9 balls, 3 white and 6 yellow.

Then the probability of obtaining a white ball from the first ballot box is:

$P (W_{u_1}) = \frac{3}{9} = \frac{1}{3}$

In the second ballot box there are 10 balls, 7 white and 3 yellow.

Then the probability of obtaining a white ball from the second ballot box is:

$P (W_{u_2}) = \frac{7}{10}$

We want to know the probability of obtaining a white ball in both urns. This is: P( $W_{u_1}$ and $W_{u_2}$ )

As the events are independent:

P( $W_{u_1}$ and $W_{u_2}$ ) = P ( $W_{u_1}$ ) * P ( $W_{u_2}$ )

P( $W_{u_1}$ and $W_{u_2}$ ) = $\frac{1}{3}* \frac{7}{10}$

P( $W_{u_1}$ and $W_{u_2}$ ) = $\frac{7}{30}$

Finally the correct option is (b) $\frac{7}{30}$

3 0

3 years ago

In a binomial distribution, n = 8 and π=0.36. Find the probabilities of the following events. (Round your answers to 4 decimal p

skelet666 [1.2K]

Answer:

$\mathbf{P(X=5) =0.0888}$

P(x ≤ 5 ) = 0.9707

P ( x ≥ 6) = 0.0293

Step-by-step explanation:

The probability of a binomial mass distribution can be expressed with the formula:

$\mathtt{P(X=x) =(^{n}_{x} ) \ \pi^x \ (1-\pi)^{n-x}}$

$\mathtt{P(X=x) =(\dfrac{n!}{x!(n-x)!} ) \ \pi^x \ (1-\pi)^{n-x}}$

where;

n = 8 and π = 0.36

For x = 5

The probability $\mathtt{P(X=5) =(\dfrac{8!}{5!(8-5)!} ) \ 0.36^5 \ (1-0.36)^{8-5}}$

$\mathtt{P(X=5) =(\dfrac{8!}{5!(3)!} ) \ 0.36^5 \ (0.64)^{3}}$

$\mathtt{P(X=5) =(\dfrac{8 \times 7 \times 6 \times 5!}{5!(3)!} ) \times \ 0.0060466 \ \times 0.262144}$

$\mathtt{P(X=5) =(\dfrac{8 \times 7 \times 6 }{3 \times 2 \times 1} ) \times \ 0.0060466 \ \times 0.262144}$

$\mathtt{P(X=5) =({8 \times 7 } ) \times \ 0.0060466 \ \times 0.262144}$

$\mathtt{P(X=5) =0.0887645}$

$\mathbf{P(X=5) =0.0888}$ to 4 decimal places

b. x ≤ 5

The probability of P ( x ≤ 5) $\mathtt{P(x \leq 5) = P(x = 0)+ P(x = 1)+ P(x = 2)+ P(x = 3)+ P(x = 4)+ P(x = 5})$

${P(x \leq 5) = ( \dfrac{8!}{0!(8!)} \times (0.36)^0 \times (1-0.36)^8 \ ) + \dfrac{8!}{1!(7!)} \times (0.36)^1 \times (1-0.36)^7 \ +$ $\dfrac{8!}{2!(6!)} \times (0.36)^2 \times (1-0.36)^6 \ + \dfrac{8!}{3!(5!)} \times (0.36)^3 \times (1-0.36)^5 + \dfrac{8!}{4!(4!)} \times (0.36)^4 \times (1-0.36)^4 \ + \dfrac{8!}{5!(3!)} \times (0.36)^5 \times (1-0.36)^3 \ )$