at a mountain village in new guinea it rains on average 6 days a week. determine the probability that it rains on
1. any one day
2. two successive days
3. three sucessive days.
what is the sample space/
A. 0.085
B.1.623
To determine the probability, we first need to understand the sample space, which represents all possible outcomes in a given situation. In this case, the sample space is the set of all possible combinations of raining and not raining for each day.
1. Any one day:
The sample space for any one day consists of two outcomes: raining and not raining. So, the sample space for any one day is {raining, not raining}.
2. Two successive days:
For two successive days, the sample space consists of four outcomes: raining on both days, not raining on both days, raining on the first day and not raining on the second day, or not raining on the first day and raining on the second day. Therefore, the sample space for two successive days is {raining, not raining} × {raining, not raining} = {(raining, raining), (raining, not raining), (not raining, raining), (not raining, not raining)}.
3. Three successive days:
Similarly, for three successive days, the sample space consists of eight outcomes: raining on all three days, not raining on all three days, in addition to the four outcomes from the two successive days, but with another day added either at the beginning or the end. Therefore, the sample space for three successive days is {raining, not raining} × {raining, not raining} × {raining, not raining}.
Now, to determine the probabilities for each scenario, we need to know the specific information regarding the likelihood of raining on each day.