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If both games cost $1 to pay? getting two heads and two tails on four coins wins you $3. or you get $2 for every six that appears when three standard dice are rolled?

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by NadinJaggi

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by NadinJaggi

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1. to play : 1 $ each game

2. 2 H + 2 T gets 3 $ on four coins game

3. 3 dice are rolled. Every 6 , gets $2.

we have to decide which game is more winning ????

*game 1: *

number of outcomes when four coins are tossed once : 2^4 = 16

Number of outcomes that are favourable = 6

( HHTT, HTHT, HTTH, TTHH, THTH, THHT ) = 4! /(2 * 2)

arrangements of 4 letters, with 2 being identical and another 2 being identical.

now Probability of winning = 6/16 = 0.375

* Expected winnings = 0.375 * $3 = $ 1.125 *

*game 2:*

number of out comes: 6^3 = 216

favourable out comes =

1. outcomes with 1 six only : 1 * 5 * 5 + 5 * 1 * 5 + 5 * 5 * 1 = 75

2. outcomes with 2 sixes : 1 * 1 * 5 + 1 * 5 * 1 + 1 * 1 * 5 = 15

3. outcomes with 3 sixes : 1 * 1 * 1 = 1

*expected winnings* = Sum of P( $2) * $2 + P($4) * $4 + P($6) * $6 + P($0) * $ 0

= ( 75/216) * $2 + (15/216) * $4 + (1/216) * $6

=*$ 1 *

* So Game 1 is better to play as the expected winnings are more.*

2. 2 H + 2 T gets 3 $ on four coins game

3. 3 dice are rolled. Every 6 , gets $2.

we have to decide which game is more winning ????

number of outcomes when four coins are tossed once : 2^4 = 16

Number of outcomes that are favourable = 6

( HHTT, HTHT, HTTH, TTHH, THTH, THHT ) = 4! /(2 * 2)

arrangements of 4 letters, with 2 being identical and another 2 being identical.

now Probability of winning = 6/16 = 0.375

number of out comes: 6^3 = 216

favourable out comes =

1. outcomes with 1 six only : 1 * 5 * 5 + 5 * 1 * 5 + 5 * 5 * 1 = 75

2. outcomes with 2 sixes : 1 * 1 * 5 + 1 * 5 * 1 + 1 * 1 * 5 = 15

3. outcomes with 3 sixes : 1 * 1 * 1 = 1

= ( 75/216) * $2 + (15/216) * $4 + (1/216) * $6

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