QUESTION 3 I [12] A student must answer a multiple-choice question with five possible answers. He knows the correct answer with
1 answer:
The probability that the student does not know the answer but he randomly guesses it is 0.146025
<h3>How to solve for the probability of having a correct guess</h3>The question has only one right answer out of 5 choices.
Probability he answers incorrectly:
1 - 0.55 * 4/5
= 0.45 * 0.8
= 0.36
Probability he does not know answer but answers the question correctly
= 0.09/0.55+0.09
= 0.140625
Read more on probability here: brainly.com/question/24756209
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We have 19 available seats, and 21 reservations.
Of the 21 reservations, 10 are sure, so we have 10 out of the 19 seats that are surely occupied.
Then, we have 9 seats for 11 reservations, each one with 44% chance of being occupied.
We have to calculate the probability that the plane is overbooked. This means that more than 9 of the reservations arrive.
This can be modelled as a binomial distirbution with n = 11 and p = 0.44, representing the 44% chance.
Then, we have to calculate P(x > 9).
This can be calculated as:
and each of the terms can be calculated as:
Then:
We have a probability of 0.18% of being overbooked (P = 0.0018).
If we want to calculate the probability of having empty seats, we need to calculate P(x<9), meaning that less than 9 of the reservations arrive.
We can express this as:
We have to calculate P(x=9) as we already have calculated the other two terms:
Finally, we can calculate:
There is a probability of 0.9875 that there is one or more empty seats.
Answer:
There is a probability of 0.0018 of being overbooked.
There is a probability of 0.9875 of having at least one empty seat.