Thread: Math Final Tomorrow! :S Probability Question.

Hello, facesonfilm!

This involves an infinite series . . .

Two hockey teams, the Spartans and the Burners, have a sudden-death
penalty shootout to decide who wins the game.
The teams take penalty shots in turns. The first team to score wins.
The probability that the Spartans score on any penalty shot is 0.3
and the probability that the Burners score on any penalty shot is 0.4.

If the Spartans take the first penalty shot,
determine the probability that they win the game.

Consider the following scenarios . . .

Spartans win on their 1st try:
. .

Spartans win on their 2nd try:
. . They miss their 1st try: .
. . The Burners miss their 1st try: .
. . The Spartans make their 2nd try: .
Spartans win on their 2nd try:
. .

Spartans win on their 3rd try:
. . They miss their 1st try: .
. . The Burners miss their 1st try: .
. . The Spartans miss their 2nd try: .
. . The Burners miss their 2nd try: .
. . The Spartans make their 3rd try: .
Sparts win on their 3rd try:
. .

Skipping the listing, we get:
. .


The probability that the Spartans win on their 1st try or their 2nd try
. . or their 3rd try or their 4th try, etc. is:



. . . . . . . . . . .

The sum of the geometric series is: .


Therefore: .