A standard die has six faces (1 through 6). The numbers greater than 4 are 5 and 6, which are 2 outcomes.
The probability of drawing a red ball is 3/5 , and the probability of drawing a blue ball is 2/5. The expected value is: E(X)=(5⋅3/5 )+(10⋅ 2/5)=3+4=8
P(X=2)=3⋅(0.5) 2 ⋅(0.5) 1 =3⋅0.25⋅0.5=3/8
There are 12 face cards in a deck (3 face cards in each of the 4 suits: J, Q, K). Out of these, 4 are queens. The conditional probability is: P(queen | face card)= total outcomes (face cards)/ favorable outcomes (queens)= 4/12= 1/3
Var(X)=4.9−(2.1) 2 =4.9−4.41=0.94
