Color Blindness Color blindness is an inherited...

Color Blindness Color blindness is an inherited characteristic that is more common in males than in females. If M represents male and C represents red-green color blindness, we use the relative frequencies of the incidences of males and red-green color blindness as probabilities to get $$ P(C)=0.039, P(M \cap C)=0.035, P(M \cup C)=0.491 $$ Source: Parsons' Diseases of the Eye. Find the following probabilities. $\begin{array}{llll}{\text { a. } P\left(C^{\prime}\right)} & {\text { b. } P(M)} & {\text { c. } P\left(M^{\prime}\right)} \\ {\text { d.P }\left(M^{\prime} \cap C^{\prime}\right)} & {\text { e. } P\left(C \cap M^{\prime}\right) \text { f. } P\left(C \cup M^{\prime}\right)}\end{array}$

Color Blindness Color blindness is an inherited characteristic that is more common in males than in females. If M represents male and C represents red-green color blindness, we use the relative frequencies of the incidences of males and red-green color blindness as probabilities to get
$$
P(C)=0.039, P(M \cap C)=0.035, P(M \cup C)=0.491
$$
Source: Parsons' Diseases of the Eye. Find the following probabilities.
$\begin{array}{llll}{\text { a. } P\left(C^{\prime}\right)} & {\text { b. } P(M)} & {\text { c. } P\left(M^{\prime}\right)} \\ {\text { d.P }\left(M^{\prime} \cap C^{\prime}\right)} & {\text { e. } P\left(C \cap M^{\prime}\right) \text { f. } P\left(C \cup M^{\prime}\right)}\end{array}$

Key Concepts

Complement Rule

The complement rule states that the probability that an event does not occur is equal to one minus the probability that the event does occur (P(A') = 1 - P(A)). This basic principle is essential when calculating probabilities associated with events’ complements.

Intersection and Union of Events

In probability, the intersection of events represents outcomes common to both events (denoted as A ? B), while the union of events represents outcomes that are in at least one of the events (denoted as A ? B). Understanding these concepts is crucial for analyzing combined events.

Inclusion-Exclusion Principle

The inclusion-exclusion principle helps calculate the probability of the union of two events by adding their individual probabilities and subtracting the probability of their intersection (P(A ? B) = P(A) + P(B) - P(A ? B)). This prevents double counting of outcomes that are common to both events.

Relative Frequency as Probability

The relative frequency approach interprets probability as the proportion of times an event occurs out of the total number of trials. This concept allows for estimating probabilities based on observed frequencies in real-world contexts.

Transcript

00:01 All right, it is given that color blindness is an inherited phenomenon and it's more common in men.

00:10 So, given that the probability of c, which is color blindness, is equals to 0 .39, and also given that the probability of being male intersection color blindness is equals to 0 .35.

00:39 And also the probability of being male or color blind is equals to 0 .491.

00:53 We then have to work a few subs.

00:57 Number 1, probability of not being colorblind or colorblind complement, which is 1 minus color blind, which gives us 0 .0 .0 .6 .6.

01:18 It's 1.

01:21 And the second part of the person says, find the probability of being male.

01:27 So we can use the definition of probability.

01:31 And we make pm the subject.

01:33 The formula meaning to say we take everything to the left end side and on that left end side we have got pm you see already waiting so we bring a plus we bring minus p c and then we add the intersection can see we are just undoing our formula and then this is emuc is given a 0 .491 minus probability of color blindness which is 0 .039 plus intersection of color blindness and male which is 0 .035.

02:30 All right so if you add and subtract you get 0 .487.

02:44 All right, then the c part of the question says, find the probability of being male complement, which is 1 minus probability of being male, which is 0 .487.

02:59 And the answer is 0 .513.

03:08 Okay.

03:09 Then we go to d...

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