Hello I would like someone to check the following answers..... 1.If you select 1

Question

Hello I would like someone to check the following answers.....

1.If you select 1 card at random from a standard deck of 52 cards (shuffled well), what is the probability of drawing:

If 1 card is drawn: A card between 3-7

If 1 card is drawn: A 5

If 1 card is drawn: A 5 or a black card
(remember, there are 2 black 5s in the deck – make sure to account for that in your calculation)

If 2 cards are drawn (without replacement): one card is a face card, the other is a 9

a• a deck of 52 cards has 4 suits,

So number of card between 3-7 = 5 * 4 = 20

so, Probability(A card between 3-7) = number of card between 3-7 / Total cards

= 20/52 = 5/13

b• number of card which are 5 = 4

Probability(card is drawn: A 5) = number of card which are 5/ Total cards

= 4/52 = 1/13

c• A 5 or a black card

total black cards = 26

remaining cards which are 5 = 2

total favourable cards = 26 +2 =28

Probability(card is drawn:A 5 or a black card) = 28 /52 = 7/13

d• one card is a face card, the other is a 9

Total face card = 12

Total 9's = 4

P(A and B) = P(A)P(B|A)

P(B|A)= Probablity of getting a 9 such that a face card has been found in the first card

P(the other is a 9)= No 9s/ Total remaining cards

= 4/51

P(one card is a face card, the other is a 9)= 12/52 * 4/51 = 48/2652

Probabity ( one card is a face card, the other is a 9) = 48/2652

2.

If you have a bag that contains 9 purple marbles, 11 black marbles, 5 red marbles, and 3 blue marbles, what is the likelihood of drawing:

If 1 marble is drawn: a blue marble

If 1 marble is drawn: a purple marble

If 1 marble is drawn: a black or a purple marble

If 2 marbles are drawn: a red and a blue (in any order)

If 2 marbles are drawn: a purple and a black (in that order)

There are 9 purple marbles, 11 black marbles, 5 red marbles, and 3 blue marbles - 28 marbles in all.

The probability of drawing a blue marble = 3/28 = 0.1071.

The probability of drawing a purple marble = 9/28 = 0.3214.

The probability of drawing a black or a purple marble = (11 + 9)/28 = 20/28 = 0.7143.

The probability of drawing a red and a blue marble = 2 * 5/28 * 3/27 = 0.0397 (Note: The 2 is for the two orders).

The probability of drawing a purple and a black marble in order = 9/28 * 11/27 = 0.1310.

Explanation / Answer

a• A deck of 52 cards has 4 suits,
So number of card between 3-7 are (4, 5, 6) = 3 * 4 = 12
So, Probability(A card between 3-7) = number of card between 3-7 / Total cards
  = 12/52 = 3/13 = 0.231

b• Number of card which are 5 = 4
Probability (card is drawn: A 5) = number of card which are 5/ Total cards
  = 4/52 = 1/13 = 0.0769

c• A 5 or a black card
total black cards = 26
remaining cards which are 5 = 2
Total favourable cards = 26 +2 =28
Probability(card is drawn:A 5 or a black card) = 28 /52 = 7/13 = 0.5385

d• one card is a face card, the other is a 9
Total face card = 12
Total 9's = 4

Probability of drawing a face card = 12/ 52 and
Probability of drawing a 9 in next attempt (without replacement) = 4/ 51 (since 1 card is already drawn)
So combined probability = (12/52) * (4/51) = 0.0181

2.

There are 9 purple marbles, 11 black marbles, 5 red marbles, and 3 blue marbles - 28 marbles in all.

The probability of drawing a blue marble = 3/28 = 0.1071

The probability of drawing a purple marble = 9/28 = 0.3214

The probability of drawing a black or a purple marble = (11 + 9)/28 = 20/28 = 0.7143

The probability of drawing a red and a blue marble = 5/28 * 3/27 = 0.0198

The probability of drawing a purple and a black marble in order = 9/28 * 11/27 = 0.131

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