Exams › GATE › Technical

Let A and B be two events in a probability space with P(A) = 0.3, P(B) = 0.5, and P(A ∩ B) = 0.1. Which of the following statements is/are TRUE?

1. The two events A and B are independent
2. P(A ∪ B) = 0.7
3. P(A ∩ B^c) = 0.2, where B^c is the complement of the event B
4. P(A^c ∩ B^c) = 0.4, where A^c and B^c are the complements of the events A and B, respectively

Correct answer: P(A ∪ B) = 0.7

Solution

The statement P(A ∪ B) = P(A) + P(B) - P(A ∩ B) simplifies to 0.3 + 0.5 - 0.1, which equals 0.7, confirming the correctness of the statement.

Related GATE Technical questions

• Which one of the following statements is FALSE?
• A user starts browsing a webpage hosted at a remote server. The browser opens a single TCP connection to fetch the entire webpage from the server. The webpage consists of a top-level index page with multiple embedded image objects. Assume that all caches (e.g., DNS cache, browser cache) are all initially empty. The following packets leave the user’s computer in some order. (i) HTTP GET request for the index page (ii) DNS request to resolve the web server’s name to its IP address (iii) HTTP GET request for an image object (iv) TCP SYN to open a connection to the web server Which one of the following is the CORRECT chronological order (earliest in time to latest) of the packets leaving the computer?
• Given an integer array of size N, we want to check if the array is sorted (in either ascending or descending order). An algorithm solves this problem by making a single pass through the array and comparing each element of the array only with its adjacent elements. The worst-case time complexity of this algorithm is
• Consider the following C program: #include <stdio.h> int main(){ int a = 6; int b = 0; while(a < 10) { a = a / 12 + 1; a += b;} printf("%d", a); return 0;} Which one of the following statements is CORRECT?
• Consider the following C program: #include <stdio.h> void fX(); int main(){ fX(); return 0;} void fX(){ char a; if((a=getchar()) != ' ') fX(); if(a != ' ') putchar(a);} Assume that the input to the program from the command line is 1234 followed by a newline character. Which one of the following statements is CORRECT?
• In a B+ tree, the requirement of at least half-full (50%) node occupancy is relaxed for which one of the following cases?

⚔️ Practice GATE Technical free + battle 1v1 →