Given a chess game has the following:
2 kings
2 queens
4 rooks
4 bishops
4 knights
16 pawns
One game piece is randomly selected, replaced, the another is chosen.
Total number of game piece = 2 + 2 + 4 + 4 + 4 + 16 = 32
To find the probability of selecting a king or queen, then pawn, first find the probability of selecting a king or queen, and the probability of selecting a pawn.
We have:
[tex]\begin{gathered} P(k\text{ or q) = }\frac{2+2}{32}\text{ = }\frac{4}{32}\text{ = }0.125 \\ \\ P(\text{pawn) = }\frac{16}{32}\text{ = }\frac{1}{2}\text{ = 0.5} \\ \\ \end{gathered}[/tex]Now, let's P(king or queen) and P(pawn):
[tex]P(k\text{ or q) and P(pawn) = 0.125 }\ast\text{ 0.5 = }0.0625[/tex]Therefore, the probability of selecting a king or queen, then a pawn is 0.0625
ANSWER:
0.0625
