Question

For \[E=\{(b,b)\}\] and \[F=\{(b,b),(g,b),(b,g)\}\], what are \[E\cap F\], \[P(E\cap F)\], and \[P(F)\]?

Options

• \[E\cap F=\{(b,b)\},\quad P(E\cap F)=\frac14,\quad P(F)=\frac34\]

• \[E\cap F=\varnothing,\quad P(E\cap F)=0,\quad P(F)=\frac34\]

• \[E\cap F=\{(b,b),(g,b),(b,g)\},\quad P(E\cap F)=\frac34,\quad P(F)=\frac14\]

• \[E\cap F=\{(g,g)\},\quad P(E\cap F)=\frac14,\quad P(F)=\frac34\]

Answer 1

The only outcome belonging to both E and F is \[(b,b)\]. One of four outcomes is in the intersection, while three of four outcomes are in F.