You walk into a clothing store and see a shirt you

Find the probability that a randomly generated bit string of length 10 does not contain a 0 if bits are independent and if:a) a

lara31 [8.8K]

Answer:

A) 0.0009765625

B) 0.0060466176

C) 2.7756 x 10^(-17)

Step-by-step explanation:

A) This problem follows a binomial distribution. The number of successes among a fixed number of trials is; n = 10

If a 0 bit and 1 bit are equally likely, then the probability to select in 1 bit is; p = 1/2 = 0.5

Now the definition of binomial probability is given by;

P(K = x) = C(n, k)•p^(k)•(1 - p)^(n - k)

Now, we want the definition of this probability at k = 10.

Thus;

P(x = 10) = C(10,10)•0.5^(10)•(1 - 0.5)^(10 - 10)

P(x = 10) = 0.0009765625

B) here we are given that p = 0.6 while n remains 10 and k = 10

Thus;

P(x = 10) = C(10,10)•0.6^(10)•(1 - 0.6)^(10 - 10)

P(x=10) = 0.0060466176

C) we are given that;

P((x_i) = 1) = 1/(2^(i))

Where i = 1,2,3.....,n

Now, the probability for the different bits is independent, so we can use multiplication rule for independent events which gives;

P(x = 10) = P((x_1) = 1)•P((x_2) = 1)•P((x_3) = 1)••P((x_4) = 1)•P((x_5) = 1)•P((x_6) = 1)•P((x_7) = 1)•P((x_8) = 1)•P((x_9) = 1)•P((x_10) = 1)

This gives;

P(x = 10) = [1/(2^(1))]•[1/(2^(2))]•[1/(2^(3))]•[1/(2^(4))]....•[1/(2^(10))]

This gives;

P(x = 10) = [1/(2^(55))]

P(x = 10) = 2.7756 x 10^(-17)

3 0

3 years ago

Ines has saved $5. She doubles the amount she saves each week. Does the function have a constant difference or a constant ratio?

salantis [7]

Answer:

The function have a constant ratio

No, it does not represent an exponential function.

Step-by-step explanation:

As given,

Ines has saved $5. She doubles the amount she saves each week.

⇒ In first week she saved = $5

In second week she saved = 2×$5 = $10

In third week she saved = 2×$10 = 20

In fourth week she saved = 2×$20 = 40

and so on..

∴ we get the series

5, 10, 20, 40 ,.......

If the series is given as a, b, c, d, ..... , then

The common difference is defined as d = b-a = c-b

The common ration is defined as r = $\frac{b}{a} = \frac{c}{b}$

Here, in the given question

The series is - 5, 10, 20, 40

This has no common difference , d = 10 - 5 (= 5 )≠ 20 - 10 (= 10)

As 5 ≠ 10

So the function does not define common difference .

Now,

This has common ratio , r = $\frac{10}{5} (=2) = \frac{20}{10}(=2)$

As 2 = 2

So, the function represent common ratio

Now,

The function does not represent an exponential function because it is increased by common ratio.

7 0

3 years ago

A tank holds 1,000 gallons of syrup. Danielle filled 65 5-gallon cans with syrup. How much syrup was left in the tank when she f

Mrrafil [7]

65 times 5 is 325 then u take 1000 and minus 325 from it and end up with 675

5 0

2 years ago

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PLZ HALP!!!!! the length of a rectange is 1 7/9 inches, and its width is 3/4 of its length. find the area of this rectangle.

11Alexandr11 [23.1K]

9514 1404 393

Answer:

2 10/27 square inches

Step-by-step explanation:

The length is 1 7/9 = 16/9 inches. The width is 3/4 of that, so is ...

(3/4)(16/9) = 4/3 inches

The area is the product of length and width, so is ...

A = (16/9 in)(4/3 in) = 64/27 in²

The area of the rectangle is 2 10/27 square inches.

7 0

3 years ago

7. Nine more than three times a mumber is -6

Vinvika [58]

Answer:

three x a mumber is 18 that is the answer

3 0

2 years ago

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