A pouch contains 59 green beads 78 red beads an 50 yellow beads how many blue beads should be added so that the probability of drawing a red bead is one third
78 = x/3
78 * 3 = 234
234 - 59 - 78 -50 = #blue beads
To solve this problem, we need to find out how many blue beads should be added to the pouch in order to make the probability of drawing a red bead one third.
Let's start by calculating the total number of beads in the pouch before adding any blue beads:
Total number of beads = Green beads + Red beads + Yellow beads
Total number of beads = 59 + 78 + 50
Total number of beads = 187
Now, let's assume that 'x' represents the number of blue beads that need to be added to the pouch. So, the new total number of beads in the pouch would be:
New total number of beads = Total number of beads + Number of blue beads
New total number of beads = 187 + x
We want the probability of drawing a red bead to be one third. The probability of drawing a red bead can be calculated as:
Probability of drawing a red bead = Number of red beads / Total number of beads
If there are 78 red beads in the pouch, the probability of drawing a red bead would be:
Probability of drawing a red bead = 78 / (187 + x)
According to the problem, this probability should be equal to one third, which can be expressed as:
78 / (187 + x) = 1/3
To solve this equation, we can cross-multiply:
3 * 78 = 1 * (187 + x)
234 = 187 + x
234 - 187 = x
47 = x
Therefore, you should add 47 blue beads to the pouch in order to make the probability of drawing a red bead one third.