Question

A game spinner has regions that are numbered 1 through 9. If the spinner is used twice, what is the probability that the first number is a 3 and the second is a 6? A. 1/18 B. 1/81 C. 1/9 D. 2/3

and The probability that a student at certain high school likes art is 36%. The probability that a student who likes art also likes science is 21%. Find the probability that a student chosen at random likes science given that he or she likes art. Round to the nearest tenth of a percent.  A. 15.0%

 B. 58.3%  C. 61.3%  D. 17.1%

Answer 1

I wanna say 1/81 because that is the smallest probability that those 2 number will get picked in that order

Answer 2

The first answer is B. 1/81

The second answer is B. 58.3%

Explanation:

`1.\thinspace Probability\thinspace of\thinspace getting\thinspace number\thinspace 3=(1)/(9)\\\\Probability\thinspace of\thinspace getting\thinspace number\thinspace 6=(1)/(9)\\\\So,\thinspace the\thinspace combined\thinspace probability\thinspace of\thinspace occurring\thinspace first\thinspace number\thinspace 3\thinspace and\thinspace second\thinspace number\thinspace 6 =(1)/(9)\cdot (1)/(9)=(1)/(81)`

`2.\thinspace Probability\thinspace that\thinspace student\thinspace likes\thinspace art, P(A) = 0.36\\\\Probability\thinspace that\thinspace student\thinspace likes\thinspace both\thinspace science\thinspace and\thinspace art, P(S\thinspace and\thinspace A) = 0.21`

`Probability\thinspace that\thinspace a\thinspace student\thinspace chosen\thinspace at\thinspace random\thinspace likes\thinspace science\thinspace given\thinspace he\thinspace likes\thinspace art :\\\\P(S\thinspace |\thinspace A)=(P(S\thinspace and\thinspace A))/(P(A))`

`\implies P(S\thinspace |\thinspace A)=(0.21)/(0.36)=0.5833`

`To\thinspace the\thinspace nearest\thinspace tenth\thinspace of\thinspace a\thinspace percent = 0.5833\cdot 100=58.33 \%`