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A and B are friends. They decide to meet between 1 PM and 2 PM on a given day. There is a condition that whoever arrives first will not wait for the other for more than 15 minutes. The probability that they will meet on that day is1. 1/42. 1/163. 7/164. 9/165. |
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Answer» Correct Answer - Option 3 : 7/16 A meeting occurs if the person arrives between 1:00 PM and 1:45 PM and the second person arrives in the next 15 minutes or if both the persons arrive between 1:45 and 2:00. Case 1: 45/60 are favorable cases and hence the probability of first-person arriving between 1:00 and 1:45 is 3/4. Probability of second person arriving in the next 15 min = 15/60 = 1/4 So, the probability of one person arriving between 1:00 and 1:45 and meeting the other = 3/4 × 1/4 × 2 = 3/8 (2 for choosing the first arriving friend) Case 2: Both friends must arrive between 1:45 and 2:00 Probability = 1/4 × 1/4 = 1/16 So, probability of a meet = 3/8 + 1/16 = 7/16 Hence, the correct answer is 7/16. |
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