9
$\begingroup$

$$\large f(0) = P(X = 0) = \frac{\binom{3}{0}\binom{17}{2}}{\binom{20}{2}} = \frac{68}{95},$$

I'm working on annotating math (probability and statistics) for the visually impaired that is to be read aloud by a screen reader and don't know what to put for this structure.

As of now, I've just got something like, "$f$ of zero equals", then I am not sure how to phrase $P(X=0)$ (is it the probability where $X = 0? $), and then really have no idea about those structures in parentheses in the quotient portion.

Thank you.

5 Answers 5

18

If this is at a beginning level:

$f$ of zero equals the probability that $X$ equals $0$; this is a fraction whose numerator is $3$ choose $0$ times $17$ choose $2$, and whose denominator is $20$ choose $2$. This evaluates to the fraction $68$ over $95$.

If the students are a bit more advanced, you can compress it a bit:

$f$ of zero equals the probability that $X$ equals $0$, which is $3$ choose $0$ times $17$ choose $2$ all over $20$ choose $2$, which simplifies to $68$ over $95$.

  • 0
    Thank you. I may have quite a few of these as I go. Is there a best place/way to ask this without becoming obtrusive? I'd Google it if I knew how but I'm not sure it's possible (even reverse image searching seems far fetched). – 2017-01-02
  • 1
    +1 I would explicitly use "the number of ways to choose..." or combinations for more clarity. Ex: the number of ways to choose $2$ items form $17$ items, or the number of combinations to choose $2$ out of $17$. – 2017-01-02
  • 6
    @Chelonian: I don’t know of any better place to ask. Perhaps by choosing judiciously you can get enough ideas from a limited number of questions to let you come up with reasonable verbalizations for the rest. – 2017-01-02
  • 10
    @msm: I’d do that only for the most inexperienced of students: there’s a point at which expanded verbiage becomes more confusing than helpful. Moreover, you want them to get used to the *n choose k* verbal construction as soon as possible. – 2017-01-02
  • 0
    Is there a downside to using "over" instead of "all over" for the division? I always thought of "all over" as a way to distinguish $(a+b)/c$ from $a+(b/c)$, or $(ab)/c$ from $a(b/c)$. Since the latter two expressions are equivalent, I'd never have thought to use "all over" to distinguish them. – 2017-01-02
  • 2
    @Vectornaut: I don’t have strong feelings either way; I simply chose the verbalization that reflects the written form. I think this slightly preferable, since the written form in turn accurately reflects the essential idea of dividing the number of (equally likely) successful outcomes by the number of possible outcomes. – 2017-01-02
  • 0
    Ah! Reflecting the written form does sound like a good idea. – 2017-01-02
7

There are so many different ways that you can do this. Fractions can be read as "[something] divided by [something else]", "numerator: [something] denominator: [something else]" or variations thereupon. Each version has its benefits, so I recommend experimenting with it. As for parenthesis, reading them out loud is not always necessary. In your example, you can get away with not reading them. Nonetheless, I think pauses after each function is helpful to the listener. Here is my recommendation:

"$f$ of $0$ [pause] equals the probability that $X$ equals $0$ [pause] equals $3$ chose $0$ [pause] times $17$ chose $2$ [pause] divided by $20$ chose $2$ [pause] equals $68$ $95^{\text{ths}}$"

3

I would read it as the probability that X equals zero, then three choose zero times seventeen choose two divided by twenty choose two.

3

"The probability that $X=0$ is equal to $3$ choose $0$ times $17$ choose $2$ in the numerator devided by $20$ choose $2$ in the denominator, which is equal to $68$ over $95$".

3

I feel that reading it like: $f (0)$ equals the probability of $X=0$ given by $3$ choose $2$ times $17$ choose $2$ divided by $20$ choose $2$ which equals $68$ over $95$. Hope it helps.

  • 0
    I'd adjust the last word "by". At least to my ear, the word "by" doesn't connote division: it could just as well refer to some form of multiplication or concatenation (e.g. "2 by 3 matrix"). – 2017-01-02
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    @ErickWong: I believe it's common in some parts of the world like India to hear "m by n" instead of "m over n", but I'm not sure why. I think it's an error due to translation. – 2017-01-02
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    Rohan, I also suggest you edit your answer. Note that "by" is used in phrases like "m by n grid" or "one by one". In the phrase "m divided by n" the prepositional phrase "by n" specifies how m is divided, and the verb "divided" cannot be omitted. – 2017-01-02