A bag contains 4 red and 5 black balls. Another bag contains 5 red, 3 ...
Introduction:
To find the probability of drawing one red and one black ball from two different bags, we need to calculate the probability of two events happening: drawing a red ball from one bag and a black ball from the other bag.
Given Information:
- Bag 1 contains 4 red and 5 black balls.
- Bag 2 contains 5 red and 3 black balls.
Probability of drawing a red ball from Bag 1:
The probability of drawing a red ball from Bag 1 can be calculated using the formula:
P(Red from Bag 1) = Number of red balls in Bag 1 / Total number of balls in Bag 1
P(Red from Bag 1) = 4 / (4 + 5) = 4/9
Probability of drawing a black ball from Bag 2:
The probability of drawing a black ball from Bag 2 can be calculated using the formula:
P(Black from Bag 2) = Number of black balls in Bag 2 / Total number of balls in Bag 2
P(Black from Bag 2) = 3 / (5 + 3) = 3/8
Probability of drawing one red and one black ball:
To find the probability of drawing one red and one black ball, we need to multiply the probabilities of the two events happening.
P(One red and one black ball) = P(Red from Bag 1) * P(Black from Bag 2)
P(One red and one black ball) = (4/9) * (3/8) = 12/72 = 1/6
Conclusion:
The probability of drawing one red and one black ball from the two bags is 1/6.