There are 4 bottles of orange juice,
3 bottles of apple juice,
2 bottles of tomato juice.
Viv takes a bottle at random and drinks the juice.
Then Caroline takes a bottle at random and drinks the juice,
Work out the probability that they both take a bottle of the same type of juice.

5/18

Step-by-step explanation:

alright what are the possibilities:

1*both take orange juice

2*both take apple

3*both take tomato

for the first option viv has 4/9 possibility of choosing orange since there are 4 orange juices out of a possible 9 then caroline comes and the new scenario is 8 bottles of which 3 are orange thus her probability of choosing orange too is 3/8. finally the combined probability of both taking orange would be 4/9 * 3/8 = 12/72

now we do the same thing for the second option of 2 apples and we get that the probability is 3/9*2/8 = 6/72

and for the third possibility it is 2/9*1/8= 2/72

now we sum the three answers above to get P=20/72 = 5/18

the reason we sum is that the event of same juice is equal to the 'sum' of the individual 3 events discussed above

so i hope this helps

answer is

In empty set, n(A) = { }.