Question

A number x is chosen at random from the numbers -3, -2,-1, 0, 1, 2, 3 the probability that |x| < 2 is:
(a) 5⁄7
(b) 2⁄7
(c) 3⁄7
(d) 1⁄7
[Note: option (c) is correct]​

Answer 1

ANSWER: you are wrong 5/7 is the answer

Explanation:

bit (a)

Answer 2

Answer:

(c) 3⁄7

Step-by-step explanation:

Probability of an event:

If the Probability of occurrence of an event E is P(E):

$\boxed{ \mathfrak{P(E) = \frac{number \: favorable \: outcomes}{total \: number \: outcomes} }}$

• number favorable outcomes meaning the total number of values of x, satisfying the given conditions.
• total number outcomes, ofcourse, means the total number of values of x given to us.

Here's, the condition imposed on x is:

|x| < 2

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Absolute Value:

(|.|) means absolute value!

that is the value of -x and +x, as long as x is same for both, i.e., x.

For example:

we have two numbers +5 and -5

|+5| = 5,

|-5| = 5

Here's it! (|.|) of both values gave the same result, I.e., it's magnitude.

Properties of absolute value function:

• It's always positive, I.e., starts from 0 and tends to infinity.
• It's equal to the set of whole numbers, I.e.,

|x| ∈ { 0, 1, 2,. .∞ }

• Absolute value function yields two values! I.e.,

|x| = +x, -x

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Back to the question:

So,

|x| < 2

==> |x| ∈ {0, 1}

[Note: 2 isn't included! That's because there's not an equal to sign wth "<". We'll not include the limit when "<" is used]

(Now, |x| = +x, and -x)

•°• |1| = +1, and -1

|0| = 0

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Probability of the given event:

That gives us 3 values of x that satisfy the condition

==> number favorable outcomes = 3

Total number of values of x = 7

==> total number outcomes = 7

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Answer:

$\mathsf{P(E) = \frac{number \: favorabe \: outcomes}{total \: number \: outcomes} }$

$\implies \mathsf{ \underline{ \: P(E) = \frac{3}{7} }}$

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Hope this helps! :)