PLEASE HELP. I will give BRAINLIEST.
Stanley has two sets of three cards face down on a table. Each set contains: the 2 of hearts, the 5 of diamonds, and the 8 of clubs. He randomly turns over one card from each set.
Find the probability of each event:

a) Both cards are red.
b) The first card is red and the second card is black.
c) Both cards are even numbers.
d) The sum of the numbers is greater than 8.

Which strategy did you use each time?
Please explain your work.`

Answer:

a =4/9  = Both cards red

b =2/9  = 1st red 2nd black

c =8/12 = 2/3  simplified even numbers

d= 8/12 = 2/3  simplified sum adds to 8

Step-by-step explanation:

a) Both cards are red see  b) 2/3 x 2/3 = 4/9

Answer 4/9

b) One of each colour red selected 1st then black

Answer = 2/3 x 1/3 = 2/9

Answer = 2/9

b) workings

(P2)Any colour RED

(P2)= S1: ( 2/3, 2/3, 1/3)

(P2) = S2: (2/3, 2/3, 1/3)

RED = 1 x 2/3 x 1/3 = 2/9 first card and second card BLACK= 1 x 1/3  = 1/3

Final = 2/9 x 1/3 = 2/9

Answer = 2/3 x 1/3 = 2/9

c)

(P3) Even numbers

(P3)= S1: ( 2/3, 1/3, 2/3)

(P3) = S2: (2/3, 1/3, 2/3)

12 events 7 outcomes see chart below as two even numbers added will always be even numbers and so will two odds including 5+5 = 10

Answer = 8/12

d)

(P4 ) Numbers that multiply to greater than 8

2 + 2  = 4

2 + 2 = 4

2 + 5 = 7

2 + 8 = 10

5 + 5 = 10

5 + 5 = 10

5 + 2  = 7

5+ 8 = 13

8 + 8 = 16

8 + 8 = 16

8 + 2 = 10

8 + 5 = 13

= 12 events either card and 8 opportunities

Answer = 8/12 simplified = 2/3

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