A probability problem by Akshit Kumar

Probability Level 3

In an entrance test there are multiple choice questions. There are four possible answers to each question of which exactly one option is correct. The probability that a student knows the answer to a question is 90 %. If he does not know the answer, he guesses randomly. Given that he gets the correct answer to a question, then the probability that he was guessing is $\frac{a}{b}$, where and b are co-prime integers. Find $a+b$.

×
{"ft_lang_label":"__label__en","ft_lang_prob":0.9450334,"math_prob":0.9753617,"size":575,"snap":"2019-43-2019-47","text_gpt3_token_len":123,"char_repetition_ratio":0.12609456,"word_repetition_ratio":0.12371134,"special_character_ratio":0.2226087,"punctuation_ratio":0.19512194,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.99986935,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2019-10-19T03:38:53Z\",\"WARC-Record-ID\":\"<urn:uuid:f775ac73-1419-465a-ac53-0907fbb4bc6b>\",\"Content-Length\":\"38455\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:33483744-5ffb-46da-9720-74ee9a5ac72f>\",\"WARC-Concurrent-To\":\"<urn:uuid:e6f67b19-6748-4a8c-a3d7-5083ff528024>\",\"WARC-IP-Address\":\"104.20.34.242\",\"WARC-Target-URI\":\"https://brilliant.org/problems/an-interesting-problem-96/\",\"WARC-Payload-Digest\":\"sha1:NEU4U3BR6D2GQOJSSIGJ2WCZJVXGF2I5\",\"WARC-Block-Digest\":\"sha1:BLOONHJQXAEKEB26LZM3HDDVBMCACIW5\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2019/CC-MAIN-2019-43/CC-MAIN-2019-43_segments_1570986688674.52_warc_CC-MAIN-20191019013909-20191019041409-00040.warc.gz\"}"}