Mathematics, 21.10.2020 01:01 alisonlebron15
A driver and a passenger are in a car accident. Each of them independently has probability 0.3 of being hospitalized. When a hospitalization occurs, the loss is uniformly distributed on [0, 1]. When two hospitalizations occur, the losses are independent. Calculate the expected number of people in the car who are hospitalized, given that the total loss due to hospitalizations from the accident is less than 1.
Answers Provided:
0.534
Step-by-step explanation:
p(0 losses) = 0.7² = 0.49
p(1 loss) = 2 x 0.3 x 0.7 = 0.42
p(2 losses) = 0.09
This is a conditional probability problem. If the number of people hospitalized is 0 or 1, then the total loss will be less than 1. However, if two people are hospitalized, the probability that the total loss will be less than 1 is 0.5. we need to exclude the 50% x 0.09 chance of a double loss costing more than 1. So
P(Cost < 1)
= 0.49 + 0.42 +0.045
= 0.955
P(0 losses | Cost < 1)
= P(0 losses and Cost < 1) / P(Cost < 1)
= 0.49 / 0.955 = 0.513
P(1 loss | Cost < 1)
= 0.42 / 0.955 = 0.440
P(2 losses | Cost < 1) = 0.045 / 0.955 = 0.047
Now take the expectation:
E[X] = (0)(0.513) + (1)(0.440) + (2)(0.047)
= 0.440 + 0.094
= 0.534
I get lost on how we know that with 1 hospitalization the total loss is less than 1.
Answers: 1
Mathematics, 21.06.2019 17:30, lizzy2951
Someone this asap for a group of students attends a basketball game. * the group buys x hot dogs at the concession stand for $2 each. * the group buys y drinks at the concession stand for $3 each. the group buys 29 items at the concession stand for a total of $70. how many hot dogs did the group buy?
Answers: 2
Mathematics, 21.06.2019 18:00, aleilyg2005
List the sides of δrst in in ascending order (shortest to longest) if: m∠r =x+28°, m∠s = 2x+16°, and m∠t = x+12°
Answers: 1
Mathematics, 21.06.2019 20:30, icantspeakengles
In priyas math class there are 10 boys and 15 girls. what is the ratio of boys to girls in priyas math class? express your answer as a decimal
Answers: 1
Mathematics, 21.06.2019 23:30, andreawright13
The complement of an angle is one-sixth the measure of the supplement of the angle. what is the measure of the complement angle?
Answers: 3
A driver and a passenger are in a car accident. Each of them independently has probability 0.3 of be...
Biology, 29.09.2019 20:10
Mathematics, 29.09.2019 20:10
Mathematics, 29.09.2019 20:10
Mathematics, 29.09.2019 20:10
History, 29.09.2019 20:10