Question

For exercises 2-4, find each probability. You can represent a probability as a fraction or decimal. 100% becomes 1 when written as a decimal, and 50% becomes 0.5.

2.)
a.) On Monday, a Meteorologist says that there is a 30% chance of rain. What is the probability that it will rain on Monday?

b.) What is the probability that it will NOT rain on Monday?

c.) On Tuesday, the Meteorologist says that there is a 0.1 probability that it will rain. What is the probability that it will NOT rain?

d.) Suppose the probability that it will rain is p. Find the probability that it will not rain today, in terms of p.

3.) A Meteorologist says that there is a 50% greater chance of rain than no rain on Wednesday. What is the probability that it will rain on Wednesday?

4.) A Meteorologist says that there is a 50% chance of rain on Saturday and a 50% chance of rain on Sunday. He concludes that it will definitely rain at least once on the weekend. Does his conclusion sound reasonable?

Answer 1

2a) The probability of rain on Monday is 30%, which can be written as 0.3.

2b) The probability of it not raining on Monday is the complement of the probability of rain, which is 1 - 0.3 = 0.7 or 70%.

2c) The probability that it will not rain on Tuesday is the complement of the probability of rain, which is 1 - 0.1 = 0.9 or 90%.

2d) If the probability that it will rain is p, then the probability that it will not rain is 1 - p.

3) If there is a 50% greater chance of rain than no rain on Wednesday, then the probability of rain is 50% + 50% * 50% = 75%.

4) The conclusion that it will definitely rain at least once on the weekend sounds reasonable because there is a 50% chance of rain on both Saturday and Sunday, so it is likely that it will rain on at least one of those days.