A standard deck contains 52 cards; without all the aces and twos, it would have 52-8=44 cards in total.
a) There are 13 heart cards in a normal deck; in this one, there are 13-2=11 heart cards; therefore,
[tex]\begin{gathered} P(heart)=\frac{11}{44}=\frac{1}{4} \\ \Rightarrow P(heart)=\frac{1}{4} \end{gathered}[/tex]
The answer to part a) is P(heart)=1/4.
b) Half of the cards in a standard deck are black; since we removed 4 red cards and 4 black cards,
[tex]P(black)=\frac{22}{44}=\frac{1}{2}[/tex]
P(black)=1/2
c) There are 12 face cards in a normal deck and none of them was removed; thus,
[tex]P(face_{})=\frac{12}{44}=\frac{3}{11}[/tex]
P(face card)=3/11
d) In general, if A is an event,
[tex]P(notA)=1-P(A)[/tex]
Therefore, in our case,
[tex]\begin{gathered} P(notHeart)=1-P(heart)=1-\frac{1}{4}=\frac{3}{4} \\ \Rightarrow P(notHeart)=\frac{3}{4} \end{gathered}[/tex]
P(not heart)=3/4
