Question

Box 1 has 2 red balls + 1 blue ball. Box 2 has 3 blue balls + 1 red ball. A coin is tossed. If it falls head up,box 1 is selected and a ball is drawn. If it falls tails up,box 2 is drawn and a ball is selected. Find the probability of selecting a blue ball

Answer 1

Answer:

13/24

Explanation:

• Box 1 has 2 red balls + 1 blue ball.

,

• Box 2 has 3 blue balls + 1 red ball.

The probability of selecting a blue ball from the boxes are:

$\begin{gathered} P(\text{blue ball from Box 1)}=\frac{1}{1+2}=\frac{1}{3} \\ P(\text{blue ball from Box 2)}=\frac{3}{3+1}=\frac{3}{4} \end{gathered}$

Next, in a coin toss, the probability of heads or tails is:

$P(H)=\frac{1}{2},P(T)=\frac{1}{2}$

To pick a blue ball, either:

• The coin falls head up AND a blue ball is selected from Box 1; OR

,

• The coin falls tails up AND a blue ball is selected from Box 2.

Thus, the probability of selecting a blue ball:

$\begin{gathered} P(\text{blue ball)=P(Head and Box 1) Or P(Tails and Box 2)} \\ =(\frac{1}{2}\times\frac{1}{3})+(\frac{1}{2}\times\frac{3}{4}) \\ =\frac{1}{6}+\frac{3}{8} \\ =\frac{13}{24} \end{gathered}$

The probability is 13/24.