Using Binomial Distribution Tables For p>0.5

The binomial tables are cumulative, so we only directly look up values of  
\[P(X \le x)\]
  for particular values of  
\[n, \: p\]
. Normally binomial tabeles are given for values of  
  up and including  
  for various values of  
. What do we do to find  
\[P(X \le 5)\]
  follows a  
We think about losses instead of wins!
  is usually taken to be the probability of a win or desirable outcome, and if this is greater than 0.5 then  
, the probability of a loss or undesirable ouytcome is less than 0.5 and we can use the tables.
Remenbers thay  
\[Losses + WINS=n\]
\[P(X \le 3)\]
  is modelled by  
The following rules apply.
\[P(X \lt x) = P(X \le x-1)\]

\[P(X \gt x) = 1-P(X \le x)\]

\[P(X \ge x) = 1-P(X \le x-1)\]

\[WINS \le 3 \rightarrow LOSSES ge 7\]

We find  
\[P(Y \ge 7\]
\[Y \sim B(10,0.4)\]

\[P(Y \ge 7)=1-P(Y \le 6)=1-0.9452=0.0548\]

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