st","extracted_subject":"MATH","extracted_chapter":"PROBABILITY","extracted_topic":"USE OF PERMUTATIONS AND COMBINATIONS IN PROBABILITY","questionPreviewUrl":"https://cdn.pureessence.tech/question-previews/packed_canvases/canvas_2222.png?top_left_x=1064&top_left_y=0&width=532&height=265&app=solveeit"},"seo_metadata":{"keywords":[]},"doubt_solver_data":{"concept_summary":[]},"embeddings":[],"is_hidden":false,"_id":"66d23e74425d76b7ab32117b","slug":"if-the-integer-a-and-b-are-chosen-at-random-betwee","content":"If the integer a and b are chosen at random between 1 and 100, then the probability that 7^a + 7^b is divisible by 5, is","options":[{"_id":"68a372e17f15af4716b4927c","text":"\$\\frac { 1 } { 4 }\$","sequence":0,"isCorrect":false},{"_id":"68a372e17f15af4716b4927d","text":"\$\\frac { 1 } { 8 }\$","sequence":1,"isCorrect":true},{"_id":"68a372e17f15af4716b4927e","text":"\$\\frac { 1 } { 7 }\$","sequence":2,"isCorrect":false},{"_id":"68a372e17f15af4716b4927f","text":"\$\\frac { 1 } { 49 }\$","sequence":3,"isCorrect":false}],"correct_answer":"$$\\frac { 1 } { 8 }$","explanation":"7^a always ends with 7, 9, 3, 1.\n\n\\7^a + 7^b is divisible by 5\n\ñ Favourable events = (25 × 25) × 2\n\nAnd sample space = 100 × 100\n\nRequired probability = \$\\frac { 2 ( 25 \\times 25 ) } { 100 \\times 100 }\$= \$\\frac { 1 } { 8 }\$","question_type":"single_choice","appeared_in":[],"created_at":"2024-08-30T21:49:40.499Z","__v":0,"vector_store_id":"7509822d-68c3-4888-812c-8743669cc0e4","updated_at":"2024-08-30T21:49:40.499Z","isStarred":false},"params":{"questionSlug":"if-the-integer-a-and-b-are-chosen-at-random-betwee"}}]}]]

Question: If the integer a and b are chosen at random between 1 and 100, then the probability that 7<sup>a</su...

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