Please Explain. Calculate the conditional probability of an event ex: A classroo
ID: 3299110 • Letter: P
Question
Please Explain.
Calculate the conditional probability of an event ex: A classroom has 16 students, of which 5 are blonde, 7 are brunette and 4 are redheads. If a student is chosen at random to leave the room and then another student is chosen at random, what is the probability that the second student chosen will be blonde given that the first student was a redhead? What is the probability that the second student chosen will be blonde given that the first student was a blonde? Calculate total probability ex: A shopper needs to visit three aisles in a supermarket. The probability that she will visit the bread aisle first is 0.36, the probability that she will visit the soup aisle first is 0.31, and the probability that she will visit the frozen foods aisle first is 0.27. If she visits the bread aisle first, the probability that she will visit the soup aisle second is 0.43. If she visits the soup aisle first, she will not visit the soup aisle again. Also, if she visits the frozen foods aisle first, the probability that she will visit the soup aisle second is 0.26. Lastly, if she visits none of the three first, the probability of her visiting the soup aisle second is 0.85. What is the total probability that the shopper will visit the soup aisle second?Explanation / Answer
13) When a redhead is chosen first, number of blondes remaining in class = 5
Total number of students remaining in class = 16-1 = 15
So, probability that the second student chosen is a blonde = 5/15 = 0.33
When first student chosen is a blonde, number of blondes remaining = 4
So, probability of selecting a bond second time = 4/15 = 0.267
14) Probability that she will visit soup isle second = probability of visiting bread isle first and soup isle second + probability of visiting frozen food isle first and first soup isle second + probability of visiting any other isle first and soup isle second
= 0.36x0.43 + 027x0.26 + (1 - 0.36 - 0.31 -0.27)x0.85
= 0.1548 + 0.0702 + 0.051
= 0.276
NB: (1 - 0.36 - 0.31 -0.27) is the probability of visiting none of the three isle first. Probability of visiting soup isle need not be considered because it is given that she wont visit the isle again.