Asingle die is rolled twice. the 36 equally-likely outcomes are shown to the right. find the probability of getting two numbers whose sum is 7

1/6

Step-by-step explanation:

When a die is rolled twice the possible outcomes are:

Here the first value represents the first outcome and the second value represents the second outcome.

S = { (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 outcomes = n(S) = 36

Let A be the event that the sum of both outcomes is 7.

A = {(1, 6) , (2,5), (3,4) , (4,3), (5,2), (6,1)}

n(A) = 6

So, P(A) = n(A)/n(S)

= 6/36

= 1/6

let soccer = x and golf = y

part a

1st equation: x + y = 125

2nd equation: x = y +45

part b

replace x in the 1st equation with the 2nd one:

y + 45 + y = 125

simplify:

2y + 45 = 125

subtract 45 from each side:

2y = 80

divide both sides by 2:

y = 80/2

y = 40

she plays golf for 40 minutes.

part c

no because she plays soccer for 45 minutes longer than golf 40 +45 =   85 minutes, not 80 minutes.

1/3

step-by-step explanation:

to find this, you can divide 12 by 4 which is 3 or you can multiply 4 until you reach 12 (4x3=12). both should give you 3, meaning theres three times less bananas than there are oranges.