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?

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)

Step-by-step 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