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belka [17]
3 years ago
14

A number is picked randomly in the range [0,7]. What is the probability that the number picked is between 3 and 5? What is the p

robability that the number picked is less than 4 knowing that the number usually picked appears to be in in the range [3,5]?
Mathematics
1 answer:
emmasim [6.3K]3 years ago
4 0

Answer:

(1) 0.125

(2) 0.125

Step-by-step explanation:

The total number of possible outcomes is:

N = 8

(1)

Compute the probability that the number picked is between 3 and 5 as follows:

Number of Favorable outcomes = 1

The probability is:

P (Number picked is between 3 and 5) = 1/8 = 0.125

Thus, the probability that the number picked is between 3 and 5 is 0.125.

(2)

The number usually picked appears to be in in the range [3,5], i.e. the numbers could be, {3, 4 or 5}.

Number of Favorable outcomes = n (Number < 4 and within [3, 5]) = 1

P (less than 4 ∩ within [3, 5]) = 1/8 = 0.125

Thus, the probability that the number picked is less than 4 knowing that the number usually picked appears to be in in the range [3,5] is 0.125.

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The answer is:  " f ⁻¹(x)  = \frac{x}{2}  + 5 " . 
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Explanation:

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Given the function:  " f(x) = 2x <span>− 10 " ;  Find the "inverse function" .

Let "f(x)" be represented by "y" ; and rewrite:

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Change the "y" to an "x" ;  and change to "x" to a "y" ; as follows:
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    x = 2y </span><span>− 10 ; 

Now, rewrite this equation, in "slope-intercept form";  that is;  "y = mx + b" ; 

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   " x = 2y </span><span>− 10 " ; 

Add "10" to each side of the equation; as follows:

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to get:

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</span>↔  2y = x + 10 ;
<span>
Now, divide each side of the equation by "2" ; 
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</span>→  2y / 2 = (x + 10) / 2 ; 
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to get: 

</span>→    y = (x/2)  + (10/2) ; 

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Now, rewrite the equation, by substituting:  " f </span>⁻¹(x) " ;  in place of the "y" ;                     to indicate that this function is an "inverse function; as follows:
 
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The answer is:  " f ⁻¹(x)  = \frac{x}{2}  + 5 " . 
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