Suppose that a person chooses a letter at random from RESERVE

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In summary, the probability of choosing the same letter at random from "RESERVE" and "VERTICAL" is 3/28. This is found by multiplying the probability of choosing a letter from "RESERVE" (1/7) by the probability of choosing the same letter from "VERTICAL" (1/8) for each of the three target letters (R, E, and V) and adding them together.
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TomJerry
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Suppose that a person chooses a letter at random from "RESERVE"

Question :
Suppose that a person chooses a letter at random from "RESERVE" and then chooses one at random from "VERTICAL" . Find the probability that the same letter is choosen.


Solution:

Probability of choosing letter from "RESERVE" is P(A) = 1/7

Probability of choosing letter from "VERTICAL" is P(B) = 1/8

Probability of choosing letter which exist in both would be P(A intersection B) = P(A) . P(B)

= 1/56 [Is this correct]
 
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  • #2
Hi TomJerry! :wink:
TomJerry said:
Probability of choosing letter from "RESERVE" is P(A) = 1/7

Probability of choosing letter from "VERTICAL" is P(B) = 1/8

Probability of choosing letter which exist in both would be P(A intersection B) = P(A) . P(B)

= 1/56 [Is this correct]

erm :redface: … on that basis, the probability of choosing the same letter from "CAT" and "MOUSE" would be 1/15 …

but it's obviously zero! :rofl:​

Start again :smile:
 
  • #3


I imagine it must be done letter by letter:
For "RESERVE"
p(R)=2/7
p(E)=3/7
p(V)=1/7

To get a match, you will need to hit the matching letter(s) in "VERTICAL".
In this case, each of the three target letters appears once, thus the probability for each of them is 1/8.

So, the odds of selecting the SAME letter in both words:
R = 2/7 * 1/8, or 2/56;
E = 3/7 * 1/8, or 3/56;
V = 1/7 * 1/8, or 1/56;

and the odds of making ANY of them is their sum 6/56, or 3/28...
 
  • #4


Datamedic, that's a good explanation, but the forum policy on homework and textbook-style questions is to give hints, not complete solutions. So keep that in mind next time, and welcome to Physics Forums.
 
  • #5


The OP seems to be spreading homework questions around in several spots outside the homework section.
 

1. What is the probability of choosing a vowel from the word RESERVE?

The probability of choosing a vowel from the word RESERVE is 3/7, or approximately 42.9%. There are 7 letters in the word and 3 of them (E, E, and E) are vowels.

2. What is the probability of choosing a consonant from the word RESERVE?

The probability of choosing a consonant from the word RESERVE is 4/7, or approximately 57.1%. There are 7 letters in the word and 4 of them (R, S, V, and R) are consonants.

3. What is the probability of choosing the letter E from the word RESERVE?

The probability of choosing the letter E from the word RESERVE is 3/7, or approximately 42.9%. There are 7 letters in the word and 3 of them are E's.

4. What is the probability of choosing a letter that is not in the word RESERVE?

The probability of choosing a letter that is not in the word RESERVE is 0. There are only 7 letters in the word and any letter chosen at random must be one of those 7.

5. If I choose a letter at random from the word RESERVE, what is the chance that it will be a vowel?

The chance of choosing a vowel from the word RESERVE is 3/7, or approximately 42.9%. This is because there are 7 letters in the word and 3 of them are vowels (E, E, and E).

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