CONDITIONAL PROBABILITY

Question

Rene and Chris went to a grocery store to buy drinks. They chose from 10 different brands of juice drinks, 6 different brands of carbonated drinks, and 3 different brands of mineral water. What is the probability that Rene and Chris both chose juice drinks, if Rene randomly chose first and liked the first brand he picked up? Show the solution.

Answer 1

(10/(10+6+3) = 10/19

(10/19)(10/19) = 100/361

Pr(both get juice drinks) = 100/361 = about 27.7% chance

similar to selection with replacement

assuming a large number of drinks availabe

but if just 19 total drinks then

the probability is

(10/19)(9/18) = 5/19 = 26.32%

similar to selection without replacement

depending on how many total drinks are available

odds are anywher from 26.32 to 27.7% probability they both get juice drinks.

the larger the number of drinks available the close the probability is to 27.7%

the smaller the number of drinks available, the closer the probability is to 26.32%