Question

1. Papa Tom Smurf is a smurf-player. He wants to take two smurfettes out on a date. There are 3 blue smurfettes, 5 navy smurfettes and 2 turquoise smurfettes.

a) What’s the probability that the smurfettes he dates are of different colours? (4)
b) If he instead takes three smurfettes out on a date, what’s the probability that they are all of the same colour? (3)

I am extremely confused with probability, can someone please help?

Answer 1

Blue -- B --- 3
Navy -- N -- 5
Turquoise -- T -- 2

a) his choices could be BN, BT, OR NT
prob(Blue Navy) = C(3,1) C(5,1)/C(10,2) = 3*5/45 = 1/3
prob(B T) = C(3,1) C(2,1)/C(10,2) = 6/45 = 2/15
prob(N T) = ...
add them up

or
Prob(B N) = (3/10) (5/9) (2) , times 2 because it could be BN or NB
= 30/90 = 1/3
etc for the other two

b) 3 of the same colour, implies it can only be BBB or NNN
combination way:
prob(BBB) = C(3,3)/C(10,3) = 1/120
other way:
prob(BBB) = (3/10)(2/9)(1/8) = 6/720 = 1/120
find NNN in the same way, then add them up