the difference in the probability of selecting 1 blue ball and 2 blue balls is 8/49 if total balls are 50,find the number of blue balls?
Answers
Answer:
10 or 40
Step-by-step explanation:
The total number of balls = 50
Let the total number of blue balls in the bag be x then :
P(getting 1 blue ball) = x/50
P(getting 2 blue balls) = x(x - 1)/50 × 49
P(getting 2 blue balls) = the probability that first ball and the second ball are blue.
x/50 - x(x - 1) / 50 × 49= 8/49
50 × 49 × 49(x) - 50 × 49 × (x² - x) = 8 × 50 × 49 × 50
Divide through by 50 × 49:
49x - x² + x = 400
-x² + 50x - 400 = 0
Divide through by - 1:
x² - 50x + 400 = 0
We solve for x since this is a quadratic equation.
The roots for this quadratic equation are :
-10 and - 40
We expand this equation as follows :
x² - 10x - 40x + 400 = 0
x(x - 10) - 40(x - 10) = 0
(x - 40)(x - 10) = 0
The value of x can be :
x = 10 or 40
This implies that the blue balls can either be 10 or 40.
Answer:
10 or 40
Step-by-step explanation:
Let say Blue Balls are B
Then Probability of Selecting 1 Blue Ball
= B/50
Then Probability of Selecting two blue Balls
= (B/50)(B-1)/49)
B/50 - (B/50)(B-1)/49 = 8/49
multiplying by 49 * 50 both sides
=> 49B - B(B-1) = 400
=> 49B - B² + B = 400
=> B² - 50B + 400 = 0
=> B² - 10B - 40B + 400 = 0
=> B(B-10) -40(B-10) = 0
=> (B-40)(B-10) = 0
=> B = 40 or B = 10
the number of blue balls = 10 or 40