Four couples are at a party. Four of the eight people are randomly selected to win a prize. No person can win more than one prize. What is the probability that both of the members of at least one couple win prizes? Express your answer as common fraction.

The probability that both of the members of at least one couple win prizes is 27/35 and this can be determined by using the given data.

Given :

The following steps can be used in order to determine the probability that both of the members of at least one couple win prizes:

Step 1 - The concept of probability is used in order to determine the probability that both of the members of at least one couple win prizes.

Step 2 - According to the given data, the total number of people is 8.

Step 3 - So, the probability that both of the members of at least one couple win prizes is:

Step 4 - Simplify the above expression.

So, the probability that both of the members of at least one couple win prizes is 27/35.

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27/35

Step-by-step explanation:

We use combination to solve for this

C(n, r), =nCr = n!/r!(n - r)!

From the question, we are told that:

Four couples are at a party. Four of the eight people are randomly selected to win a prize.

Four couples = 8 people.

= 8C4 = 8!/4! (8 - 4)!

= 70

No person can win more than one prize. ( No person can win more than one prize of the 4 people selected)

This can happen in 4 ways

[4C1 × 3C2 ] × 4=

[4!/1! ×( 4 - 1)!] × [3!/2! ×(3-2)!] × 4 ways

= 4 × 3 × 4 ways

= 48

The probability that both of the members of at least one couple win prizes

48 + 4C2/ 8C4

4C2 = 4!/2!(4 - 2) !

= 6

8C4 = 8C4 = 8!/4! (8 - 4)!

= 70

48 + 6/ 70

= 54/70

= 27/35

Therefore, the probability that both of the members of at least one couple win prizes is 27/35.

45

step-by-step explanation:

g = (2, 2)

step-by-step explanation:

given the ratio is 1 : 1 then f is the midpoint of eg

let the coordinates of g = (x, y)

using the midpoint formula

(0 + x) = 1 ( multiply both sides by 2 )

0 + x = 2 ⇒ x = 2

similarly

(4 + y) = 3 ( multiply both sides by 2 )

4 + y = 6 ( subtract 4 from both sides )

y = 2

coordinates of g = (2, 2)