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Suppose you're heading off for a long weekend (Friday, Saturday, and Sunday) somewhere and the weather report for your destination says: Chance of rain on Friday: 10% Chance of rain on Saturday: 25% Chance of rain on Sunday: 30% In each part below, find the chance exactly if it can be found using no further assumptions. If it can't be found, then (again using no further assumptions) find the best lower bound and upper bound that you can. a) the chance that it rains in your destination sometime during the long weekend

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Answer:

Probability of rain on vacation = 0.7875

Step-by-step explanation:

Given,

  • chance of rain on Friday = 10%
  • chance of rain on Saturday = 25%
  • chance of rain on Sunday = 30%

So,

Probability of rain on Friday,P(F) = 0.1

Probability of rain on Saturday, P(S) = 0.25

Probability of rain on Sunday, P(T)= 0.3

Probability of rain on both Friday and Saturday, P(F∩S)= 0.1×0.25

                                                                                           = 0.025

Probability of rain on both Friday and Saturday, P(S∩T)=0.25×0.3

                                                                                           = 0.075

Probability of rain on both Friday and Saturday, P(T∩F)=0.3×0.1

                                                                                           =0.03

Probability of rain on whole vacation, P(F∩S∩T)=0.1×0.25×0.3

                                                                               = 0.0075

Probability that there will be rain on vacation,

P(A)= P(F)+P(S)+P(T)+P(F∩S)+P(S∩T)+P(T∩F)+P(F∩S∩T)

     = 0.1+0.25+0.3+0.025+0.075+0.03+0.0075

     = 0.7875

Hence, the probability that there will be rain on vacation is 0.7875.

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