probability rule 3

Question

Events                    Relative Frequency

Clear and dry          0.2

Cloudy and dry        0.3

Rain                        0.4

Snow                       0.10

 

Based on these data, what is the probability that next Christmas will be dry?

What is the probability that next Christmas will be rainy or cloudy and dry?

Supposing next Christmas is dry, determine the probability that it will also be cloudy.

Answer 1

Presuming these events are all independent and cover all possibilities, this is an exercise in and/or probabilities. Basically keep in mind that and means to multiply, or means to add.

 

For Christmas to be dry, it could be clear and dry or cloudy and dry: 0.2+0.3 = 0.5

 

For Christmas to be rainy or cloudy and dry: 0.4 + 0.3 = 0.7

 

Presuming dry, what is the probability it will be cloudy takes a little more thought. Since the initial condition is known, our universe changes. We are limited to a total of 0.5 (0.2+0.3: the only dry options). Of that 0.3 is cloudy, so we now have 0.3 out of 0.5 possible (0.3/0.5), so the probability becomes 0.6

 

Hope this helps

 

Mike