plz can someone help me my exam is tomorrow =(

[strawberry]

hi guys I’m really stuck can someone help me plzzz

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1st:

Each letter of the alphabet is written on a different piece of paper. these pieces of paper are folded and kept in a bag. one folded paper is drawn at random from this bag.

What is the probability of selecting a vowel or a letter from the word computer??

The answer:

5|26*8|26-3|26= 5|13

And there was another question but it is not related to the 1st


2nd:

What is the probability of selecting a vowel or a letter that appears twice in the word arrangement???

The answer is:

4|11*8|11=8|26

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My question is why we used in the 1st question adding and why in the 2nd multiplying

help me

i fixed it sorry

 

[stapel]

1st: Each letter of the alphabet is written on a different piece of paper. these pieces of paper are folded and kept in a bag. One folded paper is drawn at random from this bag.

What is the probability of selecting a vowel or a letter from the word "computer"?

i) How many letters are in the bag?

ii) How many of those letters are either vowels or else some other letter from the word "computer"?

iii) Divide (ii) by (i). Reduce the fraction.

2nd: What is the probability of selecting a vowel or a letter that appears twice in the arrangement?

"In the arrangement" of what...?

My question is why we used in the 1st question adding and why in the 2nd multiplying

The forward slash, "/", is used to indicate division or fractions, and the pipe, "|", is used to indicate absolute-value bars.

(You of course have read the "Read Before Posting" thread before posting, with its links to articles on standard formatting, so you're already familiar with this formatting, I realize, but not everybody does follow instructions, sorry to say.... Kindly please pardon the repetition. )

I must confess that I'm not familiar with the back-slash notation you quoted, so I can't speak to whatever is going on in the solutions manual. Please consult with your instructor regarding clarification of this notation. Thank you!

Eliz.

 

[pka]

The answer you gave for the first part is incorrect. Here is the correct way:

\(\displaystyle \L\begin{array}{l}
C = \left\{ {c,o,m,p,u,t,e,r} \right\}\quad \Rightarrow \quad \left| C \right| = 8 \\
V = \left\{ {a,e,i,o,u} \right\}\quad \Rightarrow \quad \left| V \right| = 5 \\
C \cap V = \left\{ {e,o,u} \right\}\quad \Rightarrow \quad \left| {C \cap V} \right| = 3 \\
\left| {C \cup V} \right| = \left| C \right| + \left| V \right| - \left| {C \cap V} \right| \\
P\left( {C \cup V} \right) = \frac{8}{{26}} + \frac{5}{{26}} - \frac{3}{{26}} \\
\end{array}\)

 

[strawberry]

sorry everyone i fixed my post

thanxxxxxxxxxx

 

[soroban]

Helo, strawberry!

You're expected to know the formula:
. . \(\displaystyle P(A\,\cup\,B) \:=\(A)\,+\,P(B)\,-\,P(A\,\cap\,B)\)

In baby-talk . . . the probability of A or B happening is equal to:
. . the probability of A happening plus the probability of B happening
. . minus the probability of both A and B happening.

1) Each letter of the alphabet is written on a different piece of paper.
These pieces of paper are folded and kept in a bag.
One folded paper is drawn at random from this bag.
What is the probability of selecting a vowel or a letter from the word "COMPUTER"?

Answer: \(\displaystyle \:\frac{5}{26}\,+\,\frac{8}{26}\,-\,\frac{3}{26}\:=\:\frac{5}{13}\)

Let \(\displaystyle V\) = the letter is a vowel.
Let \(\displaystyle W\) = the letter is in the word COMPUTER.

Vowels: \(\displaystyle \:\{A,\,E,\,I,\,O,\,U\}\) . . . 5 of them.
. . \(\displaystyle P(V)\:=\:\frac{5}{26}\)

Letters in COMPUTER: \(\displaystyle \:\{C,\,O,\,M,\,P,\,U,\,T,\,E,\,R\}\) . . . 8 of them.
. . \(\displaystyle P(W) \:=\:\frac{8}{26}\)

Letters which are vowels and in COMPUTER: \(\displaystyle \:\{O,\,U,\,E\}\) . . . 3 of them.
. . \(\displaystyle P(V\,\cap\,W) \:=\:\frac{3}{26}\)

Therefore: \(\displaystyle \(V\,\cup\,W) \;=\;P(V)\,+\,P(W)\,-\,P(V\,\cap\,W) \;=\;\frac{5}{26}\,+\,\frac{8}{26}\,-\,\frac{3}{26} \;=\;\frac{10}{26}\;=\;\L\fbox{\frac{5}{13}}\)

2) What is the probability of selecting a vowel or a letter
that appears twice in the word ARRANGEMENT?

Answer: (4/11)(8/11) = 8/26 . Did you copy this incorrectly?

Let \(\displaystyle V\) = the letter is a vowel.
Let \(\displaystyle T\) = the letter appears twice in ARRANGEMENT.

Vowels: \(\displaystyle \:\{A,\,A,\,E,\,E,\}\) . . . 4 of them
. . \(\displaystyle P(V) \:=\:\frac{4}{11}\)

Double-letters: \(\displaystyle \:\{A,A,\,R,R,\,E,E\}\) . . . 6 of them
. . \(\displaystyle P(T) \:=\:\frac{6}{11}\)

Vowels and double-letters: \(\displaystyle \:\{A,A,\,E,E\}\) . . . 4 of them

Therefore: \(\displaystyle \(V\,\cup\,T) \;=\;P(V)\,+\,P(T)\,-\,P(V\,\cap\,T) \;=\;\frac{4}{11}\,+\,\frac{6}{11}\,+\,\frac{4}{11} \;=\;\L\fbox{\frac{6}{11}}\)