Total probability: a ball moved or added between draws, then a ball drawn

This type of question, asked 2 times: 2 May 2023 S1, 19 Apr 2026 S2. All 2 questions below, oldest first.

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Question 1
2 May 2023 S1
119 $A bag contains 4 Red and 6 Black balls. A ball is drawn at random from the bag, its colour is observed and this ball along with 3 additional balls of the same colour are returned to the bag. If now a ball is drawn at random from the bag, then the probability that this drawn ball is red is$
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Question 2
19 Apr 2026 S2
99 $Bag A contains 3 white and 5 black balls while bag B contains 4 white and 3 black balls. A ball is selected at random from bag A and put in bag B. If a ball is now selected at random from bag B then the probability that this ball is white ball is...$
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Question 1