Question

can u solve this....​

Answer 1

Answer:

29 / 70

Step-by-step explanation:

By the Law of Total Probability,

P(W) = P(W | WW) P(WW) + P(W | BB) P(BB) + P(W | BW) P(BW)

where just one "W" refers to drawing from bag B and two symbols "BW", "BB", "WW", refer to drawing from bag A.

Calculating the probabilities for the draw from bag A

P(WW) = (# ways getting 2 white from bag A) / (# ways of drawing 2 balls from bag A)

          = $\binom42/\binom72$

          = 6/21 = 2/7

P(BB) = $\binom32/\binom72$ = 3/21 = 1/7

P(BW) = 1 - 2/7 - 1/7 = 4/7

Calculating conditional probabilities for the draw from bag B

P(W | WW) = (# white balls in bag B after WW put in) / (# balls in bag B)

                = 5/10 = 1/2

P(W | BB) = (# white balls in bag B after BB put in) / (# balls in bag B)

              = 3/10

P(W | BW) = (# white balls in bag B after BW put in) / (# balls in bag B)

               = 4/10 = 2/5

Putting it together for the required probability

P(W) = P(W | WW) P(WW) + P(W | BB) P(BB) + P(W | BW) P(BW)

  = 1/2 × 2/7  +  3/10 × 1/7  +  2/5 × 4/7

  = 1/7  +  3/70  +  8/35

  = 10/70  +  3/70  +  16/70

  = 29 / 70