Using Binomial Distribution Tables For p>0.5
\[P(X \le x)\]for particular values of
\[n, \: p\]. Normally binomial tabeles are given for values of
\[p\]up and including
\[p=0.5\]for various values of
\[n\]. What do we do to find
\[P(X \le 5)\]if
We think about losses instead of wins!
\[p\]is usually taken to be the probability of a win or desirable outcome, and if this is greater than 0.5 then
\[1-p\], the probability of a loss or undesirable ouytcome is less than 0.5 and we can use the tables.
\[Losses + WINS=n\].
\[P(X \le 3)\]if
\[X\]is modelled by
The following rules apply.
\[P(X \lt x) = P(X \le x-1)\]
\[P(X \gt x) = 1-P(X \le x)\]
\[P(X \ge x) = 1-P(X \le x-1)\]
\[WINS \le 3 \rightarrow LOSSES ge 7\]
\[P(Y \ge 7\]using
\[Y \sim B(10,0.4)\]
\[P(Y \ge 7)=1-P(Y \le 6)=1-0.9452=0.0548\]