Question

The game of “chuck-a-luck” is played at carnivals in some parts of Europe. Its rules are as follows: You pick a number from $1\mathrm{to}6$ and the operator rolls three dice. If the number you picked comes up an all the three dice, the operator pays you $₹3$, if it comes up on two dice, you are paid $₹2$; and if it comes on just one die, you are paid $₹1$. Only if the number you picked does not come up at all, you pay the operator $₹1$. The probability that you will win money playing in this game is :

• A. $0.52$
• B. $0.753$
• C. $0.42$
• D. None of these.

Answer 1

The correct option is C

$0.42$

Explanation for the correct option:

Finding the required probability.

Let $A$ be the event that a number between $1\mathrm{to}6$ comes on a die.

$\begin{array}{rcl}& \Rightarrow & P\left(A\right)=\frac{1}{6}\left[\because P\left(A\right)+P\left(\overline{A}\right)=1\right]\\ & \Rightarrow & P\left(\overline{A}\right)=1-\frac{1}{6}\\ & =& \frac{5}{6}\end{array}$

As three dices are being rolled, so the probability that the number doesn't come on any die $\begin{array}{rcl}P{\left(\overline{A}\right)}^3& =& \frac{125}{216}\end{array}$

Therefore, the required probability is

$$\begin{gathered} =1-P{\left(\overline{A}\right)}^3 \\ =1-\frac{125}{216} \\ =\frac{91}{216} \\ \approx 0.42 \end{gathered}$$

Hence, the correct answer is option C.