Question

The weather forecast says that there is a 20% chance of rain each of the 4...

The weather forecast says that there is a 20% chance of rain each of the 4 hours during which your picnic is scheduled. What is the probability that there will be no rain in 3 of the 4 hours?

Math   Statistics-And-Probability   
0 0
Add a commentTranscribed image text
Next >

Homework Answers

Answer #1

The weather forecast says that there is a 20% chance of rain each of the 4 hours during which your picnic is scheduled. What is the probability that there will be no rain in 3 of the 4 hours?

Solution::

Let, define an event R that represent rain each of the 4 hours during which your picnic is scheduled.

So, P(R)=P(rain each hours)=20/100=1/5

P(R​​​​​​c)=P(no rain each hours)=1-1/5=4/5

We need to find,

What is the probability that there will be no rain in 3 of the 4 hours?

P(no rain in 3 of the 4 hours)

=P(1st,2nd,3rd hours no rain, 4th hours rain)+P(1st,2nd,4th hours no rain, 3rd hours rain)+P(1st,3rd,4th hours no rain, 2nd hours rain)+P(2nd,3rd,4th hours no rain, 1st hours rain)

0 0
Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Log In

Sign Up

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
Today is Sunday. Based on the weather forecast, the probability of rain on Monday, Tuesday, and...
Today is Sunday. Based on the weather forecast, the probability of rain on Monday, Tuesday, and Wednesday is 20%, 10%, and 60%, respectively. The probability of rain on both Monday and Tuesday is 5%. If it rains on Tuesday, the probability of rain on Wednesday is 75%. a. Are the events “rain on Monday” and “rain on Tuesday” independent? Explain. b. Are the events “rain on Tuesday” and “rain on Wednesday” independent? Explain.
Anyone who watches the weather on the evening news is often frustrated when the forecast for...
Anyone who watches the weather on the evening news is often frustrated when the forecast for tomorrow says sun and it rains!!!! Thinking about the weatherperson, what data sources do you think they use to come up with the probability (40% chance of rain tomorrow) when they make their forecasts?
Consider the state space {rain, no rain} to describe the weather each day. Let {Xn} be...
Consider the state space {rain, no rain} to describe the weather each day. Let {Xn} be the stochastic process with this state space describing the weather on the nth day. Suppose the weather obeys the following rules: – If it has rained for two days straight, there is a 20% chance that the next day will be rainy. – If today is rainy but yesterday was not, there is a 50% chance that tomorrow will be rainy. – If yesterday...
In Melbourne, we expect it will rain one day in a fortnight on average. Melbourne weather...
In Melbourne, we expect it will rain one day in a fortnight on average. Melbourne weather forecasters correctly predict fine weather 85% of the time and correctly predict rain 75% of the time. (a) What is the probability that the weather forecasters will forecast rain? (b) What is the probability that it will rain when the forecasters have predicted rain? Please explain why and how you get the result. Thanks so much.
Weather forecasts are generally right, but not always. For a particular winter, the local forecast predicts...
Weather forecasts are generally right, but not always. For a particular winter, the local forecast predicts rain for 35% of days and rain occurs on 38% of the days. For 25% of winter days, rain was forecast and rain does fall. Hint: Use a Venn diagram to help answer the following questions about rainy days. a) For what percentage of days does it rain without rain being forecast? b) What is the probability that there was no rain forecast nor...
Most mornings, I check the weather report before deciding whether to carry an umbrella. If the...
Most mornings, I check the weather report before deciding whether to carry an umbrella. If the forecast is “rain”, the probability of actually having rain is 70%. On the other hand, if the forecast is “no rain”, the probability of actually raining is equal to 15%. During fall and winter, the forecast is “rain”75% of the time and during summer and spring, it is 15%. a) One day, I missed the forecast and it rained. What is the probability that...
The​ day-to-day changes in weather for a certain region form a regular Markov process. Each day...
The​ day-to-day changes in weather for a certain region form a regular Markov process. Each day is​ sunny, cloudy or rainy. If it is sunny one​ day, there is a 70% chance that it will be sunny the following​ day, a 20 % chance it will be​ cloudy, and a 10 % chance of rain. If it is cloudy one​ day, there is a 50 % chance that it will be sunny the following​ day, a 30 % chance it...
A friend asks you to guess if it will rain two days in a row. If...
A friend asks you to guess if it will rain two days in a row. If you are correct on both days, your friend will pay for dinner, if you are incorrect on either day, you will have to pay for dinner. You tell your friend you think it will rain on both days. Later, you see the weather forecast for each day. There is a 70% chance of rain on the first day and a 60% chance of rain...
The Weather Channel’s forecasts are accurate about 75% of the time. Suppose the five-day forecast was...
The Weather Channel’s forecasts are accurate about 75% of the time. Suppose the five-day forecast was given. a. What is the probability that the forecast will be correct for exactly 4 days out of 5? b. What is the probability that the forecast will be correct for at least 3 days out of 5?      
Probability tells us the chance or likelihood that a particular event will occur. Whether or not...
Probability tells us the chance or likelihood that a particular event will occur. Whether or not we realize it, every day we use probability to make decisions. For instance, when deciding whether to take an umbrella, we check the weather forecast to see the probability that it will rain. In this instance, probability tells us the likelihood that it will rain; however, the decision about taking an umbrella is based on an individual’s willingness to risk getting rained on. Some...
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT