Question

Please Help!

You are at a fundraising carnival. You want to play one game and you've narrowed it down to two options, as follows:
OPTION 1: Choose a face card (K, Q, J) from a deck of cards. Then, spin an odd number on an 11-part spinner. $5 per play. Grand prize is $150.
OPTION 2: Roll two dice with a product greater than 4 and less than 12. Then, choose a numbered card from a deck of cards. $15 per play. Grand prize is $200.

Which option will you choose and why? Show your work and explain your thinking.

Answer 1

To decide which option to choose, we need to consider the probability of winning and the potential payout.

For Option 1, the probability of winning is 3/52 * 5/11 = 15/276 = 5.44%. The potential payout is $150, so the expected value of this option is:

Expected value = Probability of winning * Potential payout = 5.44% * $150 = $8.16

For Option 2, the probability of winning is 6/36 = 16.67%. The potential payout is $200, so the expected value of this option is:

Expected value = Probability of winning * Potential payout = 16.67% * $200 = $33.34

Since the expected value of Option 2 is higher than the expected value of Option 1, it is a better choice. Therefore, I would choose Option 2.