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

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)}=(1)/(1+2)=(1)/(3) \\ P(\text{blue ball from Box 2)}=(3)/(3+1)=(3)/(4) \end{gathered}`

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

`P(H)=(1)/(2),P(T)=(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)} \\ =((1)/(2)*(1)/(3))+((1)/(2)*(3)/(4)) \\ =(1)/(6)+(3)/(8) \\ =(13)/(24) \end{gathered}`

The probability is 13/24.