Question

Help pleasee!

When a golfer plays any hole, he will take 3,4,5,6, or 7 strokes with probabilities of 1/10, 1/5, 2/5, 1/5, and 1/10, respectively. He never takes more than 7 strokes.

Find the probability of:
A) Scoring 4 on each of the first three holes.
B) Scoring 3,4 and 5 (in that order( on the first three holes.
C) Scoring a total of 28 for the first four holes.
D) Scoring a total of 10 for the first three holes.

Honestly, any help is greatly appreciated; my teacher's been trying to explain over and over and I still get confused :(

Answer 1

(A) The probability of scoring 4 on each of the first three holes is
\[(\frac{1}{5})^{3}\]
(B) The probability of scoring 3, 4 and 5 on the first three holes is
\[\frac{1}{10}\times \frac{1}{5}\times \frac{2}{5}\]
There are 3! permutations of the three scores of which only one is required.
Therefore the probability of scoring 3,4 and 5 (in that order) on the first three holes is
\[\frac{1}{6}\times \frac{1}{10}\times \frac{1}{5}\times\frac{2}{5}\]