\[P(X \le x)\]
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 \[X\]
follows a \[B(10,0.6)\]
distribution?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.Remenbers thay
\[Losses + WINS=n\]
.Find
\[P(X \le 3)\]
if \[X\]
is modelled by \[B(10,0.6)\]
.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
\[P(Y \ge 7\]
using \[Y \sim B(10,0.4)\]
\[P(Y \ge 7)=1-P(Y \le 6)=1-0.9452=0.0548\]