In a new card game, you start with a well-shuffled full deck and draw 3 cards without replacement. If you draw 3 hearts, you win $50. If you draw 3 black cards, you win $25. For any other draws, you win nothing. (a) Create a probability model for the amount you win at this game, and find the expected winnings. Also compute the standard deviation of this distribution. (b) If the game costs $5 to play, what would be the expected value and standard deviation of the net profit (or loss)? (Hint: profit = winnings − cost; X − 5) (c) If the game costs $5 to play, should you play this game? Explain.

Expected pay winning $50= $0.585

Expected pay winning $25= $2.36

Expected pay for anything else= $-4.35

Expected returns=3.59

Expected value for one play= $(-1.41)

Do not play this game because you will lose $1.41

Step-by-step explanation:

Probability P(3 hearts) = (13/52)×(12/51)×(11/50) = 0.013

Probability P(3black)= (26/52)×(24/51)×(23/50) = 0.118

Probability P(drawing anything else)= 1 - 0.013 - 0.118= 0.869

Expected pay($50)= 0.013$(50-5)= $ 0.585

Expected pay($25)= 0.118(25-5)$ = $2.36

Expected pay for anything else= 0.869(0-5)$ =$(-4.347)

Expected value of one play=$ (0.585 + 2.353 -4.347) = -$1.41

c) Do not play the game.

answer:   28.56 feet (approx)

step-by-step explanation:

since, triangle abc has measure of angle c equal to 55 degrees, measure of angle abc equal to 90 degrees, and length of bc equal to 20 feet.

we have to find out the measurement of segment ab.

therefore, tan 55° =

but bc = 20 feet.

⇒ tan 55 ° =  

⇒ ab = 20 × tan 55 °

⇒ ab = 20 × 1.42814800674

⇒ ab = 28.5629601348   ≈ 28.56 feet