To plan the perfect 20th wedding anniversary, Mr. And Mrs. Sapporo need to estimate the number of guests attending and t

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To plan the perfect 20th wedding anniversary, Mr. And Mrs.
Sapporo need to estimate the number of guests attending and the
weather on the day of the event. They must consider and make
choices about the size and location of the celebration, while the
restaurant offers them options on capacity (small for less than 100
guests/medium for 100-200 guests/large for more than 200 guests)
and venue (indoor for rainy days/outdoor). Based on calculations
from wedding planners, about 5/12% chance that number of coming
guests will be less than 100 people and 25% chance that there will
be more than 200 guests coming if it rains that day. In this case,
they will need to book indoor rooms with small and large capacity,
respectively, if it rains. Fortunately, there will be more
participants if it will not rain that day, specifically, about only
12.5% chance of predicting that less than 100 guests will come and
25% chance that the number of guests will be from 100-200 people.
They are urged to pay a deposit for the restaurant to start
preparing ingredients and the menu, so they need to reconsider the
size of the party first, while the venue can be finalized later.
There's about a 30% chance of guests being under 100 people and a
40% chance of getting over 200 people.
What is the probability that it will rain that day if the coming
guest is more than 200 people?