Kirk and Les regularly play each other at darts. The probability that Kirk wins any game is 0.3 and the outcome of each game is independent of the outcome of every other game. a)Find the probability that in a match of 15 games Kirk wins

Question

b)find the expected number of game in a match of 15 games which Kirk will win
Thanks in advance

Answer 1

This is a typical case of application of the binomial distribution, which requires:
1. probability of success (0.3) is known and remains constant throughout the experiment.
2. each trial is independent of the others.
3. there are exactly two possible outcomes, success or failure (in this case).
4. the number of trials is known and remains constant, i.e. independent of outcomes.

Here n=15, p=0.3 (for Kirk),
q=(1-p)=0.7
(a) For Kirk to win, he needs to win 8 matches or more, so
P(x≥8)=P(8)+P(9)+...P(15)
(b)
expected number of success,
E[x]=μ=np