Calculate the conditional probability of an event ex: A classroom has 16 student

Question

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) P(blonde second | first redhead) = 5/(16-1) = 5/15 = 1/3

P(blonde second | blonde first) = (5-1)/(16-1) = 4/15

14) Probability that The shopper will visit soup isle second = 0.36x0.43 + 0 + 0.27x0.26 + (1 - (0.36+0.31+0.27))x0.85

= 0.276

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