Q One bag A contains 5 white and 3 black ball another bag B contains 6 white and 2 - Maths - Probability

Question

Q One bag A contains 5 white and 3 black ball another bag B
contains 6 white and 2 black balls A card drawn from the pack of
cards If It is club card a ball is drawn from bag A If It is red
card ball is drawn from bag B otherwise he kept quiet The
probability of getting white ball is?

Sanjari Kalantri · Accepted Answer

Dear Student,

Let A1 be the event of drawing a club card from the pack of cards, A2 be the event of drawing a red card from the deck of cards and A3 be the event of drawing neither a club card nor a red card from a pack of cards
Let W be the event of getting a white ball
Now, according to question,PA1 = 1352 = 14; PW  A1 = 58PA2 = 2652 = 24; PW  A2 = 68PA3 = 1352 = 14; PW  A3 = 0∴ Using the theorem of total probability,PW = PA1
PW  A1 + PA2 PW  A2 + PA3
PW  A3           = 14 × 58 + 24 × 68 + 14 × 0           = 5 + 1632 = 2132

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Q One bag A contains 5 white and 3 black ball another bag B contains 6 white and 2 black balls. A card drawn from the pack of cards. If It is club card a ball is drawn from bag A. If It is red card ball is drawn from bag B otherwise he kept quiet. The probability of getting white ball is?