a baseball team a series of five games to play, with one game each day from monday through friday. If it rains on the day of a scheduled game, the game is cancelled. There is a 20 percent probability of rain each day. how likely is it that the team will get to play at least 2 of the five games?
50 % chance
To play "at least 2" of the 5 games, each day can be considered as having .2 probability of rain or .8 probability of not raining.
The probability of playing 2 of the five is
.2*.2*.2*.8*.8.
(To get the probability of all events occurring, you multiply the individual events.)
However, since it is "at least 2," you need to consider the probability of not raining on 3, 4 or 5 days.
Calculate those in the same manner as the first alternative.
Since they can play in any one or another of these scenarios, you would add the values found for those four scenarios to get your final probability.
It may or may not be .5. Regardless, at least now you should understand the process, so you deal with similar problems in the future.
I hope this helps. Thanks for asking.
To calculate the probability of playing at least 2 of the five games, we need to consider different scenarios:
1. Playing 2 games: The probability of playing on any given day is 0.8 (not raining) and the probability of rain is 0.2. We need to multiply the probabilities for each day, so the probability of playing exactly 2 games is (0.2 * 0.2 * 0.8 * 0.8 * 0.8) = 0.02.
2. Playing 3 games: We need to consider the probability of not raining on 3 days and raining on 2 days. The probability of rain on any given day is 0.2, so the probability of no rain is 0.8. The probability of playing exactly 3 games is:
(0.2 * 0.2 * 0.8 * 0.8 * 0.8) = 0.02.
3. Playing 4 games: The probability of raining on one day is 0.2, so the probability of no rain is 0.8. The probability of playing exactly 4 games is:
(0.2 * 0.2 * 0.2 * 0.8 * 0.8) = 0.0064.
4. Playing 5 games: The probability of no rain on any given day is 0.8, so the probability of playing all 5 games is:
(0.8 * 0.8 * 0.8 * 0.8 * 0.8) = 0.32768.
To calculate the overall probability of playing at least 2 games, we sum up the probabilities of these scenarios:
0.02 + 0.02 + 0.0064 + 0.32768 = 0.37408.
So the probability of playing at least 2 of the five games is approximately 0.37408, which is 37.408%.