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Question 5NoryetanswcredMarked outOuuFlag questionOnan island_ on any day:before noon; it is twice as likely to rain than not to rain; if it rains before noon it rains afternoon with probability 0.75, ifit does not rain before noon; it rains atternoon with probabllity 0.25Pam wakes Up on the island after 1:00 PM and sees that itis currently raining Whatis the probability that F I[ Was nof rail before noon?Select one:0.14290.40000.41670.25000.5833Question 6Nol yer answeredMaireo GutOOuFlag questi
Question 5 Noryetanswcred Marked out Ouu Flag question Onan island_ on any day: before noon; it is twice as likely to rain than not to rain; if it rains before noon it rains afternoon with probability 0.75, ifit does not rain before noon; it rains atternoon with probabllity 0.25 Pam wakes Up on the island after 1:00 PM and sees that itis currently raining Whatis the probability that F I[ Was nof rail before noon? Select one: 0.1429 0.4000 0.4167 0.2500 0.5833 Question 6 Nol yer answered Maireo Gut OOu Flag question
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Solve each problem. The probability that it rains today is $4 / 5$ and the probability that it does not rain today is $1 / 5 .$ What are the odds in favor of rain?
Okay. Hey, guys, In this problem, we're told that a student is taking attend 10 multiple choice question test and each multiple choice. There's four options, and there's exactly one answer. So that means there's a 1/4 chance of truth in the correct answer and 3/4 chance of choosing a wrong answer and part A s us. One is the probability that the student gets exactly five questions, right? Getting exactly five questions right implies that there is a one fort. So since there's a one in four chance of getting one question right, there's a 1/4 chance 14 to the fifth chance, getting for exactly five right and a 3/4 to 1/5 chance of getting the remaining five wrong. But since ah, this is just assuming this basically, this probability that we just wrote down is assuming that he gets the 1st 5 right and the next five wrong. But there he can get the first. But he could get number one wrong, get the next five right and get the last four world In order to count for all those possible combinations, we're gonna have to multiply this by 10. Choose five so 10 shoes five times 14 to the fifth times 3/4 to the fifth will give us the entire probability of him getting exactly five questions. Correct. And so if we multiply that out, we use our calculator. We get that the probability is zero point 5840.584 So the probability of him it's getting exactly five questions, right? 0.584 And let's do the same process for the next problem. Getting exactly one question right? That means that probably him getting one question right is one for chance and the probability of him getting the rest of the nine questions incorrect is the re fourths to the ninth power to the ninth Power. And since uh, we don't know which question he gets incorrectly, we're gonna have to multiply this by 10. Choose one, because out of the 10 options he can get at least one correctly time. We're choosing the 11 question. He gets correctly out of those 10 options. So if we multiplied this out, that's going to give us our probability of him getting exactly one correct answer. And that probability is equivalent to 0.18 eight. And that's the answer to Part B.
If the odds on favorite friend today's Forest One, then what is the big day today? So were you in the odds for a and being big toe 4 to 1? So we want to find the probability at the door. The bottom line is for divided by most one, which is for five.
So we're assuming that the probability of having a hurricane in a given year in this area Is one out of 16 and we want to find in part a what's the probability of having a hurricane in one year followed by a hurricane in the next year. And assuming they're independent, That's going to be 116 times 1 16 And that will be won over 256. Again, that's assuming that we have independence between one year and the next. Now What happens? What's the probability that we have three hurricanes in three consecutive years and that's going to end up being 1/16 times 1, 16 times 1/16 or 1/16 to the third power, which is one out of 4096. Now we want to find, what's the likelihood that we have 10 years in a row and there is no hurricane In the next 10 years. Well, that means the probability of not having a hurricane in a given year is the complement of 1/16 which is 15 16th. And we want that to happen 10 times in a row. And the songs, we have independence. That's going to be the 15 16th to the 10th power. And that comes out to be approximately .52 Comes out to that. So about 52% chance. And for the last part we want to know what's the likelihood that we have at least one Hurricane in the next 10 years and any time we're finding the probability of at least one, 1- the probability of none will give us that probability. And so the probability of none was calculated right here. So it's going to be that compliments of our previous answer. And that comes out to be .4755. So approximately 48%. This one's about 52%,, And this one is approximately 48%.
Mhm P of the not blue is equal to the p r plus p green plus p yellow Because 0.26, 0.14, close, 0.32 is equal to 0.7.