A coin toss is used to determine which team will receive the ball at the beginning of a football game. The Cougars always choose heads in the toss. What are the odds in favor of the Cougars winning the toss in exactly two of three games?
A.3:5
B.3:8
C.5:3
D.8:3
To find the odds in favor of the Cougars winning the toss in exactly two of three games, we need to calculate the probability of that event occurring and then express it as odds.
First, let's calculate the probability of the Cougars winning the toss in exactly two of three games. We can consider each game as a separate event.
The probability of the Cougars winning the toss in a single game is 1/2, assuming a fair coin. Since they always choose heads, there is a 1/2 chance that it will be heads.
To calculate the probability of any specific combination of heads and tails in three games, we multiply the probabilities together. For two heads and one tail, the probability is (1/2) * (1/2) * (1/2) = 1/8. However, there are three different ways this combination can occur (HH, HT, TH), so we multiply the probability by 3: (1/8) * 3 = 3/8.
Now that we have the probability, we need to express it as odds. To find the odds in favor, we divide the probability of the event occurring by the probability of the event not occurring.
The probability of the event not occurring is 1 - (1/8) = 7/8.
So, the odds in favor of the Cougars winning the toss in exactly two of three games is (3/8) / (7/8) = 3/7.
Therefore, the answer is not among the given options.
I still don't get it, I mean i get odds, but this question is confusing
Thanks for all your help, I get it now
The sample space is small, let's list the outcomes:
WWW
WWL
WLW
LWW
LLW
LWL
LLW
LLL
In how many are there exactly 2 W's
So what is the probability of that happening?
Now, use the definition of "odds" to answer your question.
Be confident of your answer!
How can it be confusing? I listed the possible outcomes.
You want 2 wins out of the 8 cases. There are 3 of those, look at them.
Prob(of that event) = 3/8
Prob(NOT that event) = 5/8
Now apply your odds definition