It is given that in a group of 3 students, the probability of 2 students not having the same birthday is 0.992. What is the probability that the 2 students have the same birthday?
Given: The probability of 2 students not having the same birthday = 0.992
The events "2 students having the same birthday" and "2 students not having the same birthday" are complementary events. For complementary events, we know that P(E) + P(Ē) = 1.
Calculation: P(same birthday) = 1 - P(not same birthday) P(same birthday) = 1 - 0.992 = 0.008
Therefore, the probability that 2 students have the same birthday is 0.008.
Explanation
This question tests the concept of complementary events in probability. As shown in Example 5 (Sangeeta and Reshma's tennis match) and Example 6 (birthday problem) from the textbook, when two events are complementary (opposite), their probabilities sum to 1. The formula P(Ē) = 1 - P(E) is used. Here, 'same birthday' and 'not same birthday' are complementary events, so we simply subtract the given probability from 1.
Solution Steps
Step 1: Identify that 'same birthday' and 'not same birthday' are complementary events
Step 2: Apply the formula: P(same birthday) = 1 - P(not same birthday)
Step 3: Calculate: P(same birthday) = 1 - 0.992 = 0.008