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/
2/7
To determine the probability in each case, we need to understand the sample space, which refers to all the possible outcomes of the event being considered.
In this scenario, let's consider a week as the period of interest. Since it rains on average 6 days a week, there are 7 - 6 = 1 day when it does not rain.
1. Probability that it rains on any one day:
The sample space consists of 7 possible outcomes: {R, R, R, R, R, R, N}, where "R" represents a day when it rains, and "N" represents a day when it does not rain. Out of these 7 possible outcomes, 6 outcomes involve rain. Therefore, the probability that it rains on any one day is 6/7.
2. Probability that it rains on two successive days:
In this case, we need to consider pairs of consecutive days. The sample space now consists of 6 possible outcomes: {RR, RR, RR, RR, RR, NR}. Out of these 6 possible outcomes, 5 outcomes involve rain on two successive days. Therefore, the probability that it rains on two successive days is 5/6.
3. Probability that it rains on three successive days:
Again, we consider triplets of consecutive days. The sample space consists of 5 possible outcomes: {RRR, RRR, RRR, RRR, RNR}. Out of these 5 possible outcomes, 4 outcomes involve rain on three successive days. Therefore, the probability that it rains on three successive days is 4/5.