Question

Activity 1. TAKING CHANCES WITH EVENTS A AND B

PS:THIS IS NOT A MULTIPLE CHOICE (use probability, click the picture for example)

1.) A card is randomly drawn from a deck of 52 cards. Find the probability of drawing:
A. A red card or a spade
B. A face card or an ace
C. A diamond and a 9

2.) Two pair of dice is rolled. Determine the probability
A. P(sum is 4or11)
B. P(sum is less than 5 or sum is greater than 8)​

NONSENSE➪ REPORT
PLEASE HELP ME I NEED IT NOW

Answer 1

`\huge \mathcal{ Answer࿐}`

Question 1.) Find Probability :

A. A red card or a spade .

Total red cards = total hearts + total diamonds

• 
  `\longmapsto \: 13 + 13`

• 
  `\longmapsto \: 26`

Total spades = 13 cards

• Favourable outcomes = 26 + 13 = 39

now, probability of getting either A red card or a spade is :

`\mathrm{ (favorable \: outcomes)/(total \: outcomes) }`

• 
  `(39)/(52)`

• 
  `(3)/(4)`

B. A face card or an ace

• total face cards = 4 × 3 = 12

• total ace cards = 4

favorable outcomes = 12 + 4 = 16

The probability of getting a face card or an ace :

`\mathrm{ (favorable \: outcomes)/(total \: outcomes) }`

• 
  `(16)/(52)`

• 
  `(4)/(13)`

C. A diamond and a 9

We know there's only one diamond which is 9

So, favourable outcome = 1

Now, probability of getting a diamond and a 9 :

`\mathrm{ (favorable \: outcomes)/(total \: outcomes) }`

• 
  `(1)/(52)`

_____________________________

2.) Two pair of dice is rolled. Determine the probability :

The outcomes are :

`(1 , 1) (1 , 2) (1 , 3) (1 , 4) (1 , 5) (1 ,6)`

`(2 , 1) (2 , 2) (2 , 3) (2 , 4) (2 , 5) (2 , 6)`

`(3 , 1) (3 , 2) (3 , 3) (3 , 4) (3 , 5) (3 , 6)`

`(4 , 1) (4 , 2) (4 , 3) (4 , 4) (4 , 5) (4 , 6)`

`(5 , 1) (5 , 2) (5 , 3) (5 , 4) (5 , 5) (5 , 6)`

`(6 , 1) (6 , 2) (6 , 3) (6 , 4) (6 , 5) (6 , 6)`

Total number of outcomes = 6² = 36 outcomes

Find :

A. P (sum is 4 or 11 )

Total number of outcomes having sum of 4 is :

• 3

Total number of outcomes having sum of 11 is :

• 2

So, favorable outcome = 2 + 3 = 5

Probablity ( sum is 4 or 11 ) :

`\mathrm{ (favorable \: outcomes)/(total \: outcomes) }`

• 
  `(5)/(36)`

B. P(sum is less than 5 or sum is greater than 8)

Total number of outcomes having sum less than 5 is :

• 6

Total number of outcomes having sum greater than 8 is :

• 10

So, favorable outcomes = 10 + 6 = 16

Probablity of (sum is less than 5 or sum is greater than 8) is :

`\mathrm{ (favorable \: outcomes)/(total \: outcomes) }`

• 
  `(16)/(36)`

• 
  `(4)/(9)`

_____________________________

`\mathrm{ \#TeeNForeveR}`

Answer 2

39/52 (or 3/4)

16/52 (or 4/13)

1/52

5/36

16/36 (or 4/9)

Explanation:

1.)

A.) Let R= red S=Spade RUS= R+S-A∩S odds of getting a red card is 26/52 the odds of getting a spade is 13/52 and the odds of getting a red card and a spade is 0 (which means these events are mutually exclusive)

13/52+26/52= 39/52

B.) F=face A=Ace we want FUA= F+A-F∩A

because these two events are mutually exclusive F∩A = 0

odds of getting a face: 12/52 odds of getting an ace: 4/52

12/52+4/52= 16/52

C.) D= diamond n=nine we're looking for D∩N intuitively we know that only one card in the deck is a nine as well as a diamond so the answer must be 1/52. We can confrim this through the fact that you can find the intersection of two independent events by multiplying them. So diamond: 13/52 and n= 4/52 13/52*4/52= 1/52

2.) let F= four E= eleven

A.) we're looking for FUE or F+E-F∩E (these events are mutually exclusive which means that F∩E = 0)

I think the easiest way to solve questions like these is to list out the possible outcomes

the outcomes that add to 4 are

1,3

2,2

3,1

and therefore the probability of having a sum of 4 is 3/36

the outcomes that add to eleven are

6,5

5,6

therefore the probability of having a sum of 11 is 2/36

3/36+2/36 = 5/36

B.) same deal as the one before

list out the outcomes

less than 5

1,1

1,2

1,3

2,1

2,2

3,1

so the odds of rolling two dice and having a sum less than 5 is 6/36

Now list the outcomes where the sum is greater than 8

3,6

4,5

4,6

5,5

5,6

5,4

6,3

6,4

6,5

6,6

the odds of rolling a sum greater than 8 is 10/36

take the sum and get 16/36