The game of “chuck-a-luck” is played at carnivals in some parts of

1.	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 to 6 and the operator rolls three dice. If the number you picked comes up an all the three dice, the operator pays you RS 3, if it comes up on two dice, you are paid Rs. 2; and if it comes on just one die, you are paid Rs 1. Only if the number you picked does not come up at all, you pay the operator Rs 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» (c) 0.42 P(Particular number comes on the dice) = \(\frac{1}{6}\) (∵ there are in all 6 numbers) P(particular number does not come on the dice) = 1 - \(\frac{1}{6}\) = \(\frac{5}{6}\) As there are 3 dices, so, P(Picked number does not come in any of dice) = \(\big(\frac{5}{6}\big)^3\) P(You lose money) = \(\big(\frac{5}{6}\big)^3\) = \(\frac{125}{216}\) ≈ 0.58 ∴ P(Winning) = 1 - 0.58 = 0.42

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 to 6 and the operator rolls three dice. If the number you picked comes up an all the three dice, the operator pays you RS 3, if it comes up on two dice, you are paid Rs. 2; and if it comes on just one die, you are paid Rs 1. Only if the number you picked does not come up at all, you pay the operator Rs 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»

(c) 0.42

P(Particular number comes on the dice) = \(\frac{1}{6}\)

(∵ there are in all 6 numbers)

P(particular number does not come on the dice) = 1 - \(\frac{1}{6}\) = \(\frac{5}{6}\)

As there are 3 dices, so,

P(Picked number does not come in any of dice) = \(\big(\frac{5}{6}\big)^3\)

P(You lose money) = \(\big(\frac{5}{6}\big)^3\) = \(\frac{125}{216}\) ≈ 0.58

∴ P(Winning) = 1 - 0.58 = 0.42