Final answer:
To calculate the probability of drawing at least one red ball from a bag with 5 red and 4 blue balls in two draws without replacement, we find the complement of drawing two blue balls and subtract it from 1, which gives 5/6.
Step-by-step explanation:
We want to calculate the probability of drawing at least one red ball from a bag containing 5 red balls and 4 blue balls in two draws without replacement.
One method to solve this problem is to calculate the complement probability, which is the probability of drawing no red balls (only blue balls) and then subtract it from 1.
First, we find the probability of drawing a blue ball on the first draw, which is 4 out of 9 (since there are 4 blue and 5 red balls in total).
If a blue ball was drawn first, there are now 3 blue and 5 red balls left.
So, the probability of drawing another blue ball on the second draw is 3 out of 8.
Multiplying these probabilities gives us the probability of drawing two blue balls in a row:
P(Blue and then Blue) = (4/9) * (3/8) = 1/6
To find the probability of at least one red ball, we subtract the probability of no red balls from 1:
P(at least one red ball) = 1 - P(no red balls)
= 1 - (1/6)
= 5/6