6 A bag contains 7 red counters and 5 blue counters.
- Fred chooses 4 counters at random, without replacement. Show that the probability that Fred chooses exactly 2 red counters is \(\frac { 14 } { 33 }\).
- Lina chooses 4 counters at random from the bag, records whether or not exactly 2 red counters are chosen, and returns the counters to the bag. She carries out this experiment 99 times.
(a) Find the mean of the number of experiments that result in choosing exactly 2 red counters.
(b) Find the variance of the number of experiments that result in choosing exactly 2 red counters. - Alex arranges all 12 counters in a random order in a straight line.
A is the event: no two blue counters are next to one another.
B is the event: all the blue counters are next to one another.
Find \(\mathrm { P } ( A \cup B )\).