Mike and Dave play the following game. Mike Pickls a card from a deck of cards. If he selects an ace, Dave gives him 5 dollars. If not, he gives Dave 2 dollars. Determine Mikes and Daves expectation

OneClass: Mike and Dave play the following game. Mike Pickls a card from a deck of cards. If he selec...

PROBLEM 21: A casino game involves shuffling a standard deck of 52 playing cards, and then randomly selecting one of the cards from the shuffled deck. If the selected card is an Ace, the player wins $1, and if not, the player wins nothing. If 104,000 people play the game once each during a given day at the casino, how many of them should we expect to win the game? A) 800 B) 16,000 C) 8,000 D) 2,000 E) none of the above

Pete and two co-workers harvested 18 pumpkins from a farm where they worked. If each person harvested at least 5 pumpkins, what's the probability that Pete harvested at least 7 pumpkins?

A. ³⁄₁₀

B. ¹⁄₅

C. ⁷⁄₁₀

D. ¹⁄₁₀

Three cards are drawn from a standard 52-card deck of cards without replacement. What's the probability that the third card drawn is a heart if the first two cards were also hearts?

A. ¹¹⁄₅₁

B. ²⁶⁄₅₂

C. ¹³⁄₅₂

D. ¹¹⁄₅₂

In the city of Savannah, Georgia, 22% of young couples take wedding pictures along the Riverwalk (R), and 42% of young couples take wedding pictures in one of the many historical squares (S) throughout the city. However, only 14% of young couples take wedding pictures along the Riverwalk and in the squares. Are these two events independent of each other? Include the reason why or why not.

A. The events aren't independent, because P(R) × P(S) ≠ P(P and S).

B. The events are independent, because P(R) × P(S) ≠ P(P and S).

C. The events aren't independent, because P(R) × P(S) = P(P and S).

D. The events are independent, because P(R) × P(S) = P(P and S)

graywalrus187

Mr and Mrs Spin operate a Ferris Wheel at various shows and carnivals. A passenger sits in a capsule and enjoys the ride and views. Below is a diagram showing their magnificent wheel:

Passengers embark and disembark the capsule from the platform (a maximum of 6 passengers are allowed at any given time). The time for a passenger to enter the capsule and return to the platform is 6x minutes. The process repeats until the final passenger(s) embark at no later than 10 pm each evening. The Ferris Wheel runs in an anti-clockwise direction. The height h, in metres, from the ground to a capsule, is measured from the ground to the ball on top of any capsule. It is modelled by 𝒉(𝒕) = 𝒂 − 𝐛cos (𝝅/ 𝟑) A passenger pays 3y dollars for a ride on the wheel. The variables a, b, x and y are as follows: § a is equal to 14 (i.e. a=14) § b is equal to the last digit of your student id plus 2 (e.g. if your id is 4567891 then b=3). § x is equal to the third digit of your id plus 3 (e.g. if your id is 4567891 when x=9). § y is equal to the month that you are born plus 6 (e.g. if you are born in July then y=13). Mr and Mrs Spin would like you to do the following mathematical analysis and present the results in a report for their consumption.

Task 1:

What are the minimum and maximum height of a capsule on the Ferris Wheel?

Task 2:

Determine the heights of each of the capsules on the Ferris Wheel while passengers either embark or disembark a capsule. Present these heights in table form, with appropriate labelling.

Task 3:

Determine the time when the final passenger(s) will disembark the capsule and the Ferris Wheel cease for the evening (remember that the final passengers will embark no later than 10 pm). Note, it is possible that the final passenger(s) may embark the capsule prior to 10 pm, so the answer to this task may not be 10 pm + 6x.

Task 4:

Evaluate the number of capsules that will have a passenger(s) embark for any day, given the Ferris Wheel will commence at 4 pm and the time for passenger(s) to embark and disembark is considered negligible.

ochredinosaur493

Mike and Dave play the following game. Mike Pickls a card from a deck of cards. If he selects an ace, Dave gives him 5 dollars. If not, he gives Dave 2 dollars. Determine Mikes and Daves expectation

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