You play the following game from a well-shuffled deck of 52 cards. If you draw a

Question

You play the following game from a well-shuffled deck of 52 cards. If you draw a black
card, you win $1. If you draw a heart, you win $4. For any diamond, you win $7, plus an
additional $15 for the king or ace of diamonds.
1. Create a probability model for the amount you win playing this game. Find the expected value and standard deviation for this model.

2. On average, what is the most a person should be willing to pay to play this game if the
goal is to make a profit?

3. Assume there is no fee to play. If you play the game each day of the week (7 days/week),
what do you expect your weekly earnings to be? What is the standard deviation of the
weekly totals?

Explanation / Answer

probability of winning $1 =P(X=1)=P( of black card) =26/52 =1/2

probability of winning $4 =P(X=4) =P( heart) =13/52=1/4

probability of winning $7 =P(X=7) =P( dioamond except king or ace) =11/52

probability of winning $22 =P(X=22) =P( ace or king of diamond)=2/52=1/26

hence below is probability distribution of X:

1)

from above expected value =3.83

standard deviation =4.34

2) for make a profit the most a person should be willing to pay is expected alue =3.83

3) expected weekly earnings =7*3.83=26.788

and std deviation =4.34*(7)1/2 =11.4825

x p(x) xP(x) x2P(X) (x-)2 (x-)2P(x) 1 1/2 0.500 0.500 7.991 3.996 4 1/4 1.000 4.000 0.030 0.007 7 11/52 1.481 10.365 10.068 2.130 22 1/26 0.846 18.615 330.261 12.702 total 1 = 3.83 33.481 348.351 2= 18.8354 std deviation=     =    2 = 4.3400

Related Questions

Navigate

• Browse (All)
• Browse Y
• Subjects

---

---

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