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3 years ago

Help me..

Mathematics

1 answer:

Rufina [12.5K]3 years ago

4 0

Can you post a clearer pic please??

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Consider two independent tosses of a fair coin. Let A be the event that the first toss results in heads, let B be the event that

aliina [53]

Answer with Step-by-step explanation:

We are given that two independent tosses of a fair coin.

Sample space={HH,HT,TH,TT}

We have to find that A, B and C are pairwise independent.

According to question

A={HH,HT}

B={HH,TH}

C={TT,HH}

$A\cap B=$ {HH}

$B\cap C$ ={HH}

$A\cap C$ ={HH}

P(E)= $\frac{number\;of\;favorable\;cases}{total\;number\;of\;cases}$

Using the formula

Then, we get

Total number of cases=4

Number of favorable cases to event A=2

$P(A)=\frac{2}{4}=\frac{1}{2}$

Number of favorable cases to event B=2

Number of favorable cases to event C=2

$P(B)=\frac{2}{4}=\frac{1}{2}$

$P(C)=\frac{2}{4}=\frac{1}{2}$

If the two events A and B are independent then

$P(A)\cdot P(B)=P(A\cap B)$

$P(A\cap)=\frac{1}{4}$

$P(B\cap C)=\frac{1}{4}$

$P(A\cap C)=\frac{1}{4}$

$P(A)\cdot P(B)=\frac{1}{2}\cdot \frac{1}{2}=\frac{1}{4}$

$P(B)\cdot P(C)=\frac{1}{4}$

$P(A)\cdot P(C)=\frac{1}{4}$

$P(A)\cdot P(B)=P(A\cap B)$

Therefore, A and B are independent

$P(B)\cdot P(C)=P(B\cap C)$

Therefore, B and C are independent

$P(A\cap C)=P(A)\cdot P(C)$

Therefore, A and C are independent.

Hence, A, B and C are pairwise independent.

6 0

3 years ago

Mr. Wong is a history teacher. In order to study how his 1st period class did on a 100-point test, he made the stem-and-leaf plo

s344n2d4d5 [400]

Answer:

The answer is D and B trust me 100%

Step-by-step explanation:

8 0

4 years ago

The perimeter of a rectangle must be less than 172 feet. If the length is known to be 53 feet, find the range of possible widths

dlinn [17]

The interval notation for width of rectangle will be: (1,33)

Step-by-step explanation:

Perimeter of rectangle < 172 feet

Length of rectangle = 53 feet

Width of rectangle = ? (range of values)

The formula used to find perimeter of rectangle is:

$Perimeter=2l+2w$

where l is length and w is width

In our case we will use: $2l+2w$ because perimeter should be less than 172

Putting values:

$2l+2w$

So, width should be less than 33

Since width should be positive and greater than 0

So, the interval notation for width of rectangle will be: (1,33)

Keywords: Perimeter of rectangle

Learn more about Perimeter of rectangle at:

#learnwithBrainly

3 0

3 years ago

Daniel bought 8 pairs of socks and a tshirt. The t-shirt cost $15.

Kisachek [45]

8x + 15 = 31

Or

16 + 15 = 31

Not entirely sure if this is what you were asking for but I hope this helps!

5 0

3 years ago

Find the quotient of x-8 over x-10 by inspection.

Andru [333]

$\frac{x-8}{x-10}$

$\frac{x-10+2}{x-10}$

$\frac{x-10}{x-10}+\frac{2}{x-10}$

$1 + \frac{2}{x-10}$

7 0

3 years ago