Answer:
P(A) = p1
(1 − q1q2)
Step-by-step explanation:
Let A = player A wins,
then P(A) = p1 + (1 − p1)(1 − p2)P(A)
⇒ P(A) = p1
(1 − q1q2)
Q1: 479 001 600 ways
Explanation:
You have 12 people, 12 seats, ¹²P₁₂ ways in arranging them, or essentially 12! ways
Q2: 1 036 800 ways
Explanation:
Let's break it up into two cases.
Case 1: BGBGBGBGBGBG
Case 2:GBGBGBGBGBGB
Let's deal with case 1, because case 2 will pop out. There are ⁶P₆ ways in sorting out the boys and ⁶P₆ ways in sorting out the girls, so for case 1, we'd have (⁶P₆)² ways in sorting out boys and girls in case 1.
This is exactly the same in case 2, so it'd be (⁶P₆)² ways in sorting out girls and boys in case 2.
So, (⁶P₆)² + (⁶P₆)² ways = 1 036 800 ways if they alternate
It is B because you have to subtract and than you have to add
The pool's dimension are l = 2.7 m and w = 1.2 m
Step-by-step explanation:
Step 1 :
Given
The pool's perimeter = 7.8 m
Four times the pool's length = nine times the pool's width.
=> 4l = 9w => l = (
) w
Where l is the pool's length and w is the pool's width
Step 2:
The rectangle's formula for perimeter is 2 (l+w)
Substituting l = (
) w ,
2[ (
) w + w] = 7.8 (given)
(
) w = 7.8 = > w = 1.2 m
Step 3 :
l = (
) w = (
) 1.2 = 2.7
l = 2.7 m
Step 4 :
Answer :
The pool's dimension are l = 2.7 m and w = 1.2 m
Answer:
Distance between the police station and the fire station be 4 miles
Step-by-step explanation:
Let distance between the police station and the fire station be x miles.
The distance between the library and the police station is 3 miles less than twice the distance between the police station and the fire station.
Distance between the library and the police station 
Also, distance between the library and the police station is 5 miles.
