Chapter 10, Problem 13CT

a.

To determine

To calculate:

The probability that any one choose a black or queen piece.

Answer to Problem 13CT

The probability that any one choose a black or queen piece $0.53$ .

Explanation of Solution

Given information:

	King	Queen	Bishop	Rook	Knight	Pawn
Black	$1$	$1$	$2$	$2$	$2$	$8$
White	$1$	$1$	$2$	$2$	$2$	$8$

Formula used:

  $P\left(AorB\right)=P\left(A\right)+P\left(B\right)-P\left(AandB\right)$

Calculation:

	King	Queen	Bishop	Rook	Knight	Pawn
Black	$1$	$1$	$2$	$2$	$2$	$8$
White	$1$	$1$	$2$	$2$	$2$	$8$

Assume, event $A$ is chess piece is black piece and event $B$ is queen. Of these $1$ outcome is common to both $A$ and $B$ are any two events then probability of $A$ and $B$ is as follows:

  $P\left(AorB\right)=P\left(A\right)+P\left(B\right)-P\left(AandB\right)$

From the given information,

  $P\left(A\right)=\frac{16}{32},P\left(B\right)=\frac{2}{32}$

The required probability is as follows:

  $\begin{array}{l}P\left(AorB\right)=P\left(A\right)+P\left(B\right)-P\left(AandB\right)\\ =\frac{16}{32}+\frac{2}{32}-\frac{1}{12}\\ =0.53\end{array}$

So, the probability that any one choose a black or queen piece $0.53$ .

b.

To determine

To calculate:

The probability that anyone chooses a king then pawn.

Answer to Problem 13CT

The probability that anyone chooses a king then pawn is $0.56$ .

Explanation of Solution

Given information:

	King	Queen	Bishop	Rook	Knight	Pawn
Black	$1$	$1$	$2$	$2$	$2$	$8$
White	$1$	$1$	$2$	$2$	$2$	$8$

Formula used:

  $P\left(AorB\right)=P\left(A\right)+P\left(B\right)$

Calculation:

	King	Queen	Bishop	Rook	Knight	Pawn
Black	$1$	$1$	$2$	$2$	$2$	$8$
White	$1$	$1$	$2$	$2$	$2$	$8$

Assume event $A$ is chess piece is king and event $B$ is pawn. Because, you do not replace first marble before drawing the second one, the events are dependent.

The required probability is as follows:

  $\begin{array}{l}P\left(AorB\right)=P\left(A\right)+P\left(B\right)\\ =\frac{2}{32}+\frac{2}{32}\\ =0.56\end{array}$

So, the probability that anyone chooses a king then pawn is $0.56$ .