Question

6 blue chips, 3 white chips and 4 re chips are placed in a bag. 3 chips are drawn without replacement. what is the probability at least one of the chips is red?

Answer 1

Given that, there are 6 blue chips, 3 white chips and 4 red chips.

Total number of chips = 6 + 3 + 4 = 13

3 chips can be selected from 13 chips by, ¹³C₃ = 286 ways

We want to find, P(at least one red chip)

P(draw at least one red chip) = 1 - P(draw zero red chip)

Number of ways that zero red chip can be slected from 4 red chips = ⁴C₀ = 1

and other 3 chips can be selected from remaining 9 chips by,

⁹C₃= 84 ways

Therefore, P(draw zero red chip) = 84/286 = 0.293706

Hence,

P(draw at least one red chip) = 1 - 0.293706 = 0.706294

Therefore, the probabilityat least one of the chip is red is 0.706294