Math Lab
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Probability: Drawing from a Bag

Probability · Class X

A bag has R red and B blue balls; compute the probability of each colour on one draw.

5
type a value
030
7
type a value
030
Live values
  • Total balls12
  • P(red)0.4167
  • P(blue)0.5833
  • P(red) + P(blue)1
xy
  • P(red) as blue count varies

Formulas in this lab

  • Total balls
    R+BR + B
  • P(red)
    R/(R+B)R/(R+B)
  • P(blue)
    B/(R+B)B/(R+B)
  • P(red) + P(blue)
    =1= 1
Tip: Adding more blue balls dilutes P(red) toward zero in a smooth 1/(R+x) curve.

Frequently asked questions

▶How do we compute simple probabilities?

If a bag has R red and B blue balls, the chance of drawing red on one pull is $P(\text{red}) = \frac{R}{R + B}$ and similarly for blue. The two probabilities add up to 1, since exactly one colour must come out.

▶How do I use this lab?

Slide the number of red and blue balls. The lab shows $P(\text{red})$ and $P(\text{blue})$ as fractions and decimals. Try R = 5, B = 7 to see 5/12 and 7/12.

▶Common mistake on this topic

Students write the probability as $\frac{R}{B}$ instead of $\frac{R}{R+B}$, forgetting that the denominator is the total number of balls. Also, probability is dimensionless - never write it with units.

▶Where do we use this idea?

Lottery tickets, kabaddi raid selections, and lucky-draw boxes at melas all use this formula. If a Diwali lucky-dip has 50 winning slips out of 500, your chance of a prize on one try is 1/10.