LOTS OF POINTS

Imagine a standard deck of cards with all of the aces and twos removed. Find each probability below.

a) P(heart)

b) P(black)

c) P(face card)

d) How is the P(face card) different with this deck from the probability if the deck was not missing any cards? Which probability is greater? Why?

e) P(not heart)

There are 26 black cards (club, spade, 13 of each). We take out 2 of clubs, ace of clubs, 2 of spades, ace of spades. We're left with 26-4 = 22 black cards.

There are 44 total cards as computed earlier in part a above

22/44 = 1/2

Which effectively says "half of the cards are black"

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Part c)

There are 3 face cards (jack, queen, king) for any one suit. There are 4 suits. So there are 3*4 = 12 face cards.

Divide the number of face cards (12) over the total number of cards after we take out the aces and twos (44). So we have 12/44 = 3/11

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Part d)

If we didn't take out any cards, then we have 12 face cards out of 52 total so 12/52 = 3/13, basically saying 3 out of every 13 cards is a face card.

Let's compare the two fractions 3/11 and 3/13

I'm going to put a double question mark between the two fractions because at this point I don't know which one is larger (or even if they are equal or not)

3/11 ?? 3/13

3*13 ?? 3*11 ... cross multiply

39 ?? 33

That last step has 39 on the left side being larger. So we can replace every double question mark with a "greater than" sign. This is what it would look like after you've done so

3/11 > 3/13

3*13 > 3*11 ... cross multiply

39 > 33

Since the last inequality is true, the first inequality is true. So 3/11 is larger. The probability from part c is larger.

Using a calculator, we can see that

3/11 = 0.2727

3/13 = 0.2308

So this confirms that 3/11 is larger than 3/13.

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Part e)

Subtract the result of part a from 1

1 - (answer from part a) = 1 - (1/4) = 3/4

This rule works because you either get a heart card, or you don't get a heart card. This is the rule of probability complements.

bratislava bratislava · Answer 2 · 2022-01-12T06:08:57+01:00

As per the standard deck of cards that has all aces and 2 cards are removed. The probability of the first card is heart, the second of a black and the third card is a face card.

As there are 13 hearts, but we take out 2 cards ( hearts, ace of hearts) we get 13-2 = 11 left. Then, there are two cards removed in every suit (2 ace cards) totaling 2*4 = 8 cards removed.

So 52-8 = 44 cards are leftover. Divide the two values: 11/44 = 1/4. We're left with 26-4 = 22 black cards. A 44 total cards as collected earlier in part a above that is 22/44 = 1/2.

Similarly, we get 1/4 , b) 1/2 , c) 3/11 , d) 3/13, e) 3/4.

Learn more about the deck of cards with all of the aces and twos removed.

brainly.com/question/22433948.