The odds against a volleyball team winning a game are 5:3. What is the probability, as a reduced fraction, that they will win the game?
total chances = 8
5 to lose
3 to win, so
p(win) = 3/8
To find the probability, we need to convert the odds against winning to a fraction.
The odds against winning are given as 5:3. This means that for every 5 unfavorable outcomes, there are 3 favorable outcomes.
To convert this to a fraction, we add the two numbers of the odds together: 5 + 3 = 8.
The probability of winning the game is then the favorable outcomes divided by the total outcomes: 3/8.
So, the probability that the volleyball team will win the game, as a reduced fraction, is 3/8.
To find the probability, you can use the formula:
Probability (P) = 1 / (Odds against + 1)
In this case, the odds against the volleyball team winning the game are 5:3. To calculate the probability, we need to convert the odds into a single number by adding the two parts of the ratio:
Odds against = 5 + 3 = 8
Now, we can use the formula:
P = 1 / (8 + 1)
= 1 / 9
Therefore, the probability that the volleyball team will win the game, as a reduced fraction, is 1/9.