2English and American spellings are colour and color, respectively
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20/02/2024, 15:38
English and American spellings are colour and color, respectively. A man staying at a Parisian hotel writes - brainly.com
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English and American spellings are colour and color, respectively. A man staying at a
Parisian hotel writes this word, and a letter taken at random from his spelling is found to be
a vowel. If 40 percent of the English-speaking men at the hotel are English and 60 percent
are Americans, what is the probability that the writer is an Englishman?
babij907
09/16/2019
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Mathematics
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20/02/2024, 15:38
English and American spellings are colour and color, respectively. A man staying at a Parisian hotel writes - brainly.com
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Expert-Verified Answer
No one rated this answer yet — why not be the first? Probability of an event is the measure of its occurrence
. The probability that the writer is
an Englishman is 0.45 approx.
How to calculate the probability of an event?
Suppose that there are finite elementary events in the sample space of the considered
experiment
, and all are equally likely.
Then, suppose we want to find the probability of an event E.
Then, its probability is given as
where favorable
cases are those elementary events who belong to E, and total cases are
the size of the sample space
.
What is chain rule in probability?
For two events A and B, by chain rule, we have:
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20/02/2024, 15:38
English and American spellings are colour and color, respectively. A man staying at a Parisian hotel writes - brainly.com
https://brainly.com/question/13275973
3/8
For the given case, we can take the things in terms of event
. Taking the given things as
events, we get:
A = Event of that person writing the word being English
B = Event of that person writing that word being an American
C = Event of picking a vowel from the word that person writes
.
Then, as it is given that 40 percent of the English
-
speaking men at the hotel are English
and 60 percent are Americans
,
thus, P(A) = 40% = 0.40
and P(B) = 60% = 0.60
Also, using the conditional probability
, we get that:
P(C|A) = 3/6 = 0.5 (C|A means A is given, it means it is specified that the word written is
"
colour
" It has 3 vowels and 6 total letters
)
similarly, we get P(C | B) = 2/5 = 0.4
Now, using the chain
rule
, we get:
The needed probability is that probability that the writer is an Englishman
given that the letter taken at random was found to be vowel
.
It is written symbolically as: Using the law of total probability
, we got:
Thus, using the chain rule
, we get:
Thus, the probability that the writer is an Englishman is 0.45 approx.
Learn more about probability here:
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20/02/2024, 15:38
English and American spellings are colour and color, respectively. A man staying at a Parisian hotel writes - brainly.com
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Answer:
The probability is 5/11
Step-by-step explanation:
Let's call V the event that the letter taken at random is a vowel.
Let's call E the event that the man is English and A to the event that the man is American.
If 40 percent of the English-speaking men at the hotel are English means P(E)=0.40 and
60 percent are Americans means P(A)=0.60
In ''color'' we have 2 vowels out of 5 letters so P(V/A)=2/5
In ''colour'' we have 3 vowels out of 6 letters so P(V/E)=3/6=1/2
P(E/V)=P(E
∩
V)/P(V)
P(V)=P(V|E)P(E) +P(V|A)P(A)
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20/02/2024, 15:38
English and American spellings are colour and color, respectively. A man staying at a Parisian hotel writes - brainly.com
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P(V)=(1/2)0.40+(2/5)0.60=0.44
P(E
∩
V)=P(V|E)P(E)=(1/2)0.40=0.20
P(E/V)=0.20/0.44=0.45454545=5/11
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