A box contains blue chips and red chips. A person selects two chips without replacement. If the probability of selecting a blue chip and a red chip is , and the probability of selecting a blue chip on the first draw is , find the probability of selecting the red chip on the second draw, given that the first chip selected was a blue chip.

Question

A box contains blue chips and red chips. A person selects two chips without replacement. If the probability of selecting a blue chip and a red chip is  , and the probability of selecting a blue chip on the first draw is  , find the probability of selecting the red chip on the second draw, given that the first chip selected was a blue chip.

Quizplus · Accepted Answer

We know that the probability of selecting a blue chip on the first draw is P(B) = 11eaa984_72bc_9510_97c0_872d7751565c_TB1705_11. Let R be the event of selecting a red chip on the second draw, given that the first chip selected was a blue chip. We need to find P(R|B).

We can use Bayes' theorem:

P(R|B) = P(B and R) / P(B)

We are given that P(B and R) = 11eaa984_72bc_950f_97c0_492b4e0503a1_TB1705_11. So now we just need to find P(B).

P(B) = probability of selecting a blue chip on the first draw
     = 11eaa984_72bc_9510_97c0_872d7751565c_TB1705_11

Now we can substitute into the formula for Bayes' theorem:

P(R|B) = (11eaa984_72bc_950f_97c0_492b4e0503a1_TB1705_11) / (11eaa984_72bc_9510_97c0_872d7751565c_TB1705_11)

Simplifying, we get:

P(R|B) = 11eaa984_72bc_e334_97c0_27c97764e03f_TB1705_11

So the answer is D.

A Box Contains Blue Chips and Red Chips