Numinum
Answered

Get the answers you need at Westonci.ca, where our expert community is always ready to help with accurate information. Our platform provides a seamless experience for finding precise answers from a network of experienced professionals. Get detailed and accurate answers to your questions from a dedicated community of experts on our Q&A platform.

FAST PLEASE
A standard deck of 52 playing cards contains 13 cards in each of four suits: hearts, diamonds, clubs, and spades. Four cards are drawn from the deck at random. What is the approximate probability that exactly three of the cards are diamonds? 1% 4% 11% 44%

Sagot :

Answer:  B)  4%

=====================================================

Explanation:

We'll involve the nCr combination formula here. This is because order doesn't matter.

There are n = 13 diamonds and we want to select exactly r = 3 of them.

So,

[tex]_n C _r = \frac{n!}{r!*(n-r)!}\\\\_{13} C _{3} = \frac{13!}{3!*(13-3)!}\\\\_{13} C _{3} = \frac{13!}{3!*10!}\\\\_{13} C _{3} = \frac{13*12*11*10!}{3!*10!}\\\\_{13} C _{3} = \frac{13*12*11}{3!}\\\\_{13} C _{3} = \frac{13*12*11}{3*2*1}\\\\_{13} C _{3} = \frac{1716}{6}\\\\_{13} C _{3} = 286\\\\[/tex]

There are 286 ways to pick the three diamond cards. Then there are 52-13 = 39 ways to pick the fourth card that is either a spade, club of heart.

So we have 286*39 = 11,154 ways to pick the four cards given the conditions your teacher set.

This is out of 52C4 = 270,725 ways to pick four cards (use the nCr formula above with n = 52 and r = 4).

Divide the two values to get the answer:

(11,154)/(270,725) = 0.04120048019208

that rounds to 0.04 which converts to 4%

So there's roughly a 4% chance of getting exactly 3 diamond cards.

iLoveMathAndEnglish

Answer:

4% (four percent)

We appreciate your time on our site. Don't hesitate to return whenever you have more questions or need further clarification. Thanks for using our platform. We aim to provide accurate and up-to-date answers to all your queries. Come back soon. Thank you for visiting Westonci.ca. Stay informed by coming back for more detailed answers.