Question

This time of year, if today has snow, there is a 40% chance that there will be snow tomorrow, and a 30% chance that there will be rain but not snow tomorrow. If today has rain but not snow, there is a 50% chance of rain but not snow tomorrow, and a 20% chance of snow. If there is neither snow nor rain today, there is a 10% chance of snow tomorrow, and a 20% chance of rain but not snow. a) There is neither snow nor rain today. What is the probability of snow the day after tomorrow? b) It is raining today, but there is no sign of snow. What is the probability of either rain or snow (or both) the day after tomorrow?

Answer 1

a) The probability of snow the day after tomorrow if there is neither snow nor rain today is 15% (0.15)

b) The probability of either rain or snow (or both) the day after tomorrow if it is raining today but there is no sign of snow is 58% (0.58)

Explanation:

a) There is neither snow nor rain today.

Tomorrow

• 10% chance snow

• 20% chance rain

• 70% chance neither snow nor rain

The day after tomorrow is snow

• 10% chance snow × 40% chance snow or

• 20% chance rain × 20% chance snow or

• 70% chance neither rain nor snow × 10% change snow

In total:

• (0.10 × 0.40) + (0.20 × 0.20) + ( 0.70 × 0.10) = 0.15

b) It is raining today, but there is no sign of snow.

Tomorrow

• 50% chance of rain

• 20% chance of snow

• 30% chance neither snow nor rain

either rain or snow (or both) the day after tomorrow

• (50% chance of rain×50% chance of rain)+(50% chance of rain×20% chance of snow)

• (20% chance of snow×40% chance of snow)+(20% chance of snow×30% chance of rain)

• (30% chance neither snow nor rain×10% chance of snow)+(30% chance neither snow nor rain×20% chance of rain)

In total:

• (0.50×0.50)+(0..50×0.20)+(0.20×0.40)+(0.20×0.30)+(0.30×0.10)+(0.30×0.20) =0.25+0.10+0.08+0.06+0.03+0.06=0.58