Question

David Beckham takes 3 penalty kicks, and the results (G for “goal” or M for “miss”) are
recorded (in order). Write out the set that represents each of the following events, and then
find the probability of each event, assuming he has a 90% of scoring a goal on each kick.
a) Missing all 3
b) Scoring 1 out of 3
c) Scoring on all 3
d) Making no more than 1 out of 3

Answer 1

a) The probability of a goal on each kick is 0.9. Therefore the probability of a miss on each kick is 1.0 - 0.9 = 0.1.
P(G) = 0.9
P(M) = 0.1
The result of each kick is independent of the results of other kicks. Therefore the multiplication theorem applies:
P(3 misses) = P(M) * P(M) * P(M) = ?

b) The probability of scoring one out of three can be found from the binomial distribution:
\[P(OneGoal)=\left(\begin{matrix}3 \\ 1\end{matrix}\right)\times 0.9\times (0.1)^{2}=?\]