Question 112034
 It is known that 10% of all people are left handed. A sample of 10 students is selected at random. What is the probability that 2 of these 10 students is left handed? Find the probability that none of the students are left handed? 

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No, I'm afraid you're off the track.  These are BINOMIAL problems!  

You can use any of these three methods:

Method 1. Calculate it by the formula:

P(exactly x out of n) = {{{n!/(x!(n-x)!)}}}{{{p^x*(1-p)^(n-x)}}}

where n = the number of trials = 10
      p = the probability of selecting one lefty in one trial, 10% or .1
      x = the number you want to find the probability of getting,
          which is 2 in the first problem and 0 in the second.

P(exactly 2 out of 10) = {{{10!/(2!(10-2)!)}}}{{{.1^2*(1-.1)^(10-2)}}}
P(exactly 2 out of 10) = {{{10!/(2!8!)}}}{{{.1^2*.9^8}}}
P(exactly 2 out of 10) = {{{3628800/(2*40320)}}}{{{.01*.43046721}}}
P(exactly 2 out of 10) = {{{.1937102445}}}

For the second problem:

P(exactly 0 out of 10) = {{{10!/(0!(10-0)!)}}}{{{.1^0*(1-.1)^(10-0)}}}
P(exactly 0 out of 10) = {{{10!/(0!10!)}}}{{{.1^0*.9^10}}}
P(exactly 0 out of 10) = {{{3628800/3628800)}}}{{{1*.3486784401}}}
P(exactly 0 out of 10) = {{{.3486784401}}}

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Method 2.  Look it up in the binomial probability table in the
           back of your book.

1. Find the section of that table that reads n = 10. 
2. Read across until you come to p = 0.1
3. Run your finger down that column until to see 2 on the far left
   of your finger.
   A. If you read .1937 then that's the answer, for you have an "exact
      value" table.
   B. If you read .9298 then you have a "cumulative value" table, so
      1. Find the number directly above that one in the table, which will
         have 1 at the far left, and read .7361.
      2. Subtract .9298 - .7361 and get .1937

For the second problem

1. Find the section of that table that reads n = 10. 
2. Read across until you come to p = 0.1
3. Run your finger down that column until to see 0 on the far left
   of your finger, and read .3487. (That should be the very first
   entry in that column)

(Note: it makes no difference which kind of table you have
for 0, since there is no cumulation for 0)

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Method 3.  TI-83 or 84 graphing calculator

For your first problem:

1. Press 2nd VARS ALPHA MATH
   You should see this on your screen:     binompdf(
2. Type in 10,.1,2) so that you see this:  binompdf(10,.1,2)
3. Press ENTER and read .1937102445

For your second problem:

1. Press 2nd VARS ALPHA MATH
   You should see this on your screen:     binompdf(
2. Type in 10,.1,0) so that you see this:  binompdf(10,.1,0)
3. Press ENTER and read .3486784401

Edwin</pre>