Question

Weather forecasts are generally right, but not always. For a particular winter, the local forecast predicts rain for 35% of days and rain occurs on 38% of the days. For 25% of winter days, rain was forecast and rain does fall.

Hint: Use a Venn diagram to help answer the following questions about rainy days. a) For what percentage of days does it rain without rain being forecast?
b) What is the probability that there was no rain forecast nor did it rain?
c) On what percentage of days was there either rain or rain forecast?

d) If it is raining, what is the probability that rain was forecast?
e) Are rain and forecast for rain mutually exclusive events? Explain.

f) Are rain and forecast for rain independent events? Explain.

Answer 1