The odds of any event A occurring are given by P(A)/P(A\') while the odds agains

Question

The odds of any event A occurring are given by P(A)/P(A') while the odds against any event A occurring are given by P(A')/p(A). I nthe game of craps, two fair dice are rolled and the sum of hte faces showing is computed.

A. One bet in the game of craps is the "Yo" bet; this is a bet the next roll will be an eleven. If the bet were a fair one, the payout of the bet would be the odds against rolling an eleven on the next roll. Find the true odds against rolling an eleven on the next roll (i.e., find the odds a player "should" receive).

B. In reality, the bet pays 15 to 1. Based off of these odds. find the implied probability of rolling an eleven on the next roll.

C. Is the Yo bet a good bet? Why of why not?

Explanation / Answer

A. P(rolling an eleven) = P(5,6) + P(6,5)

= 2/36

= 1/18

P(not rolling an eleven) = 1 - 1/18

= 17/18

Odds against rolling an eleven = 17/18 : 1/18

= 17 to 1

B. Implied probability of rolling 11 = 1/(1+15)

= 1/16

C. Yo bet is not a good bet. The mplied probability is greater than the actual probability. This means, according to the bet, it is shown that there is more chance of winning that the actual winning probability. So, when u do a Yo bet, the actual chance of winning is less and you are more likely to lose money, i.e, you expected return will be negative, indicating a loss.

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.