Q. In an examination mark obtained by Arun is between 10 to 24, and marks obtained by Varun is between 7 to 19. Marks obtained by Varun are a prime number while marks obtained by Arun are even integers.<\/p>
Which of the following statement(s) is\/are True?<\/p>
I. Probability of sum of marks obtained by both is prime number is 1\/2<\/p>
II. Probability that difference of marks obtained by both is even number, is 0<\/p>
III. Probability of sum of marks obtained by both, is perfect square is 1\/6<\/p>
A. II only<\/p>
B. I and II only<\/p>
C. II and III only<\/p>
D. I only<\/p>
E. None of these<\/p><\/p>\n\n\n\n
Ans: I and II only<\/span><\/p>\n\n\n\n Sol:<\/p>\n\n\n\n Marks obtained by Arun = [12, 14, 16, 18, 20, I. Probability of sum of marks obtained by both is Q. In an examination mark obtained by Arun is between 10 to 24, and marks obtained by Varun is between 7 to 19. Marks obtained by Varun are a prime number while marks obtained by Arun are even integers. Which of the following statement(s) is\/are True? I. Probability of sum of marks obtained by both […]<\/p>\n","protected":false},"author":419,"featured_media":162680,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[5138],"tags":[5139],"offerexpiration":[],"class_list":["post-162679","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-quantitative-aptitude","tag-quantitative-aptitude"],"_links":{"self":[{"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/posts\/162679","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/users\/419"}],"replies":[{"embeddable":true,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/comments?post=162679"}],"version-history":[{"count":1,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/posts\/162679\/revisions"}],"predecessor-version":[{"id":162681,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/posts\/162679\/revisions\/162681"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/media\/162680"}],"wp:attachment":[{"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/media?parent=162679"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/categories?post=162679"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/tags?post=162679"},{"taxonomy":"offerexpiration","embeddable":true,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/offerexpiration?post=162679"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
22]
Marks obtained by Varun = [11, 13, 17]
Possible sum of marks = [23, 25, 29, 25, 27, 31,
27, 29, 33, 29, 31, 35, 31, 33, 37, 33, 35, 39]<\/p>\n\n\n\n
prime number is 1\/2.
In 10 cases we get sum is prime = [23, 29, 31,
29, 29, 31, 31, 31, 37]
Total outcomes = 18
Required probability = 9\/18 = 1\/2
II. Probability that difference of marks obtained
by both is even number is 0
Marks obtained by Arun are an even number,
while Varun is an odd number.
Even \u2013 odd = odd
So required probability = 0
III. Probability of the sum of marks obtained by
both is a perfect square.
In two cases we get sum is perfect square = [25,
25]
Required probability = 2\/18 = 1\/9
Only I and II is true
Hence answer is option B<\/p>\n\n\n\n