8 votes 8 votes A man has three cats. At least one is male. What is the probability that all three are male? $\frac{1}{2}$ $\frac{1}{7}$ $\frac{1}{8}$ $\frac{3}{8}$ Probability cmi2012 probability + – go_editor asked May 22, 2016 go_editor 1.9k views answer comment Share Follow See all 0 reply Please log in or register to add a comment.
Best answer 10 votes 10 votes Answer is (B) Given that $A$ man has three cats and At least one is male. Possible combination for at least one cat is male=$(M,F,F),(F,M,F),(F,F,M),(M,F,M),(M,M,F),(F,M,M),(M,M,M)$ Probability that all three are male=$\frac{1}{7}$ LeenSharma answered May 23, 2016 edited Sep 25, 2018 by Krithiga2101 LeenSharma comment Share Follow See all 8 Comments See all 8 8 Comments reply Show 5 previous comments priyanka manwani commented Oct 8, 2018 reply Follow Share why order is important in this question??? here it is not mentioned that which one numbered should be male or female???? 1 votes 1 votes Vishnathan commented Aug 18, 2019 reply Follow Share How the order got importance in this question? After all the man owns three cats and one of them is male then $(M,F,F) ,(F,M,F), (F,F,M)$ is same isn't it? 0 votes 0 votes Gaurav Yadav commented Sep 6, 2020 reply Follow Share I still couldn’t understand why we need to consider all arrangements. 0 votes 0 votes Please log in or register to add a comment.
15 votes 15 votes P(all 3 males / atleast one male) = P(all 3 males AND atleast one male) / P(atleast one male) = P(all 3 males) / P(atleast one male) = P( (all 3 males) / [1-P(no males] ) = (1/8) / (1-1/8) = (1/8) / (7/8) = 1/7 Vicky rix answered Sep 24, 2017 Vicky rix comment Share Follow See 1 comment See all 1 1 comment reply tusharp commented Apr 24, 2019 reply Follow Share Awesome. More intuitive. 0 votes 0 votes Please log in or register to add a comment.
0 votes 0 votes Option B is the correct It is a que of conditional probability so probability that atleast one is male A = c(3,1)/8 probability that atleast two are male B=c(3,2)/8 probability that atleast three male C= c(3,3)/8 p(atleast one is male)=A+B+C/8 =7/8 All 3 are male p(All 3 are male)=1/8 so total prob =p(All 3 are male)/p(atleast one is male) = 1/7 Pradeep A answered Oct 9, 2018 Pradeep A comment Share Follow See all 0 reply Please log in or register to add a comment.
0 votes 0 votes Let A be the event that at least one cat is Male. Let B be the event that all the three cats are Male. By conditional probability: $P(B|A) = \frac{P(B\cap A)}{P(A)}$ => If you think about it, $P(B\cap A)=P(B)$ because $A \subset B$ So, our equation is reduced to $P(B|A) = \frac{P(B)}{P(A)}$ => $ \frac{1/8}{7/8}$ => $ \frac{1}{7}$ JashanArora answered Jan 9, 2020 JashanArora comment Share Follow See all 0 reply Please log in or register to add a comment.