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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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Final answer:

The probability that it will rain at least once on a weekend with varying rain chances each day cannot be found by adding probabilities. To estimate this, calculate the combined chance of no rain throughout the weekend and subtract it from 100%. The result for the given percentages is a 52.75% chance of rain during the weekend.

Step-by-step explanation:

Understanding Probability in Weather Forecasts

When looking at the chance of rain during a long weekend with different percentages each day, we cannot simply add the probabilities to find the overall chance of rain. Instead, the best method to estimate the probability of it raining at least once during the weekend is to calculate the probability that it does not rain on any of the days and subtract this from 100%.

For the individual chances of no rain: Friday (90%), Saturday (75%), and Sunday (70%), we multiply these probabilities together to find the cumulative chance of no rain all weekend, which gives us: 0.9 * 0.75 * 0.7 = 0.4725, or 47.25%. Thus, the probability of it raining at least once during the weekend is 1 - 0.4725 = 0.5275, or 52.75%.

Addressing the incorrect statements:

a. A 60% chance of rain on Saturday and a 70% chance on Sunday does not result in a 130% chance over the weekend. Probabilities cannot exceed 100%, indicating that this statement is erroneous.

b. The probability that a baseball player hits a home run cannot be directly compared to the probability of getting a hit without knowing specific statistics. Home runs are a subset of hits, so naturally, the chance of any hit is higher than a home run specifically.

User Bakoyaro
by
4.8k points
4 votes

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.

User Luismartingil
by
6.2k points
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