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

Answer:

The first answer is B. 1/81

The second answer is B. 58.3%

Step-by-step explanation:

$1.\thinspace Probability\thinspace of\thinspace getting\thinspace number\thinspace 3=\frac{1}{9}\\\\Probability\thinspace of\thinspace getting\thinspace number\thinspace 6=\frac{1}{9}\\\\So,\thinspace the\thinspace combined\thinspace probability\thinspace of\thinspace occurring\thinspace first\thinspace number\thinspace 3\thinspace and\thinspace second\thinspace number\thinspace 6 =\frac{1}{9}\cdot \frac{1}{9}=\frac{1}{81}$

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

$Probability\thinspace that\thinspace a\thinspace student\thinspace chosen\thinspace at\thinspace random\thinspace likes\thinspace science\thinspace given\thinspace he\thinspace likes\thinspace art :\\\\P(S\thinspace |\thinspace A)=\frac{P(S\thinspace and\thinspace A)}{P(A)}$

$\implies P(S\thinspace |\thinspace A)=\frac{0.21}{0.36}=0.5833$

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