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In a coin and die game, you roll a fair six-sided die and toss a coin. If you roll a 6 and toss a tails, you gain $110. Otherwise, you lose $10. If you were to play the game 45 times, how much money can you expect to gain or lose?

Respuesta :

Answer:

$0

Explanation:

Probability of getting a six and a tail:

= (1 ÷ 6) × (1 ÷ 2)

= 1 ÷ 12

Probability of not getting a six and a tail:

= 1 - (1 ÷ 12)

= (11 ÷ 12)

Therefore, the expected value is as follows:

= (Probability of getting a six and a tail × Gain) - (Probability of not getting a six and a tail × Lose)

= [(1 ÷ 12) × $110] - [(11 ÷ 12) × $10]

= $0

Hence,

For 45 times,

Money expected = 45 × $0

                            = $0