Please show work .. how do you solve it 4. [12) Two fair dice are rolled, and th
ID: 3046671 • Letter: P
Question
Please show work .. how do you solve it 4. [12) Two fair dice are rolled, and the sum of the numbers of dots on the top faces is the value of a random variable X. Find: (a) P(x - 7): (b) P(x 12)). irdivariable :Find: (a) P((X = 7}); (b) P(,- 5. [16] Three radar detectors A, B, and C, for detecting speeding vehicles on a highway work independently. Radar detector A has a failure probability 0.02, radar detector B has a failure probability 0.03, and radar detector C has a failure probability 0.04. (a) What is the probability that all three detectors fail to detect a speeding vehicle? (b) What is the probability that only radar detector A detected the speeding vehicle? 6, [16] of the travelers arriving at an airport, 70% fly on m ajor domestic airlines, 20% fly on other domestic airlines, and 10% travelers fly on foreign airlines. Of those traveling on m ajor airlines, 60% are traveling for business reasons, whereas 50% of those traveling on other domestic airlines, and 75% of those traveling on foreign airlines are traveling for business reasons. A traveler arriving at the airport is randomly selected. What is the probability that the person- (a) is traveling on business? (b) is traveling for business on a non-major domestic airlines? (c) arrived on a non-major domestic airline, given that the person is traveling for business reasons? (d) is traveling on business, given that the person arrived on a foreign airline plane?Explanation / Answer
Q4
Concept Base
When two fair dice are rolled, there are 36 possible combinations of the number of dots on the top two faces. These are:
(1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6), (2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6), ………….,
(6, 1), (6, 2), (6, 3), (6, 4), (6, 5), (6, 6).
Given X = sum of the number of dots on the top two faces, to evaluate the probability of a particular sum we only need to enumerate the cases out of the above 36 cases where the two numbers add to the required sum and divide that number of cases by 36.
Now, to get the answers for the asked questions:
Part (a)
P(X = 7) = (The number of cases where the two numbers add to 7)/36
= {(1, 6), (2, 5), (3,4), (4, 3), (5, 2), (6,1)}/36
= 6/36
= 1/6 ANSWER
Part (b)
P(X = 12) = (The number of cases where the two numbers add to 12)/36
= {(6, 6)}/36
= 1/36 ANSWER