a) Marie has a bag of sweets which are all identical in shape. The bag contains 6 orange drops and 4 lemon drops. She selects one sweet at random, eats it, and then takes another at random. Draw a...

1. a) Marie has a bag of sweets which are all identical in shape. The bag contains 6 orange drops and 4  lemon drops. She selects one sweet at random, eats it, and then takes another at random. Draw a  fully label tree diagram.

Determine the probability that:

(i)both sweets are orange drops.

(ii)both sweets are lemon drops

(iii)the first is an orange drop and the second is a lemon drop

(iv)the first is a lemon drop and the second is an orange drop.

(v)both sweets are orange drops given that the second is an orange drop.

1. b) The data set 33, 18, 25, 40, 36, 41,
   m,
   n
   has a mode of 36 and a mean of 32. Find
   m
   and
   n
   given  that
   m
   >
   n. Hence find the variance.


2. c) Consider the data set {8, 11, 12, 9,
   a}.

(i) Find the value of
a
if the mean of the data set is 13.

(ii) Hence calculate the standard deviation of the data