Question

Is the answer consistent will wit Problem 3: Two bags contain 3 red & 7 black, and 4 rad & 6 black balls respectively. One of the was selected at random and a ball is drawn from it. If the hall drawn is red, find the probability in drawn from the second bag. What do I know? What do I want to find out? What do we expect the answer to be? How do I go from what I know to what I want to find? Is the answer consistent with what I expected? Problem 4: In a certain game, you perform three tasks. heads. You roll a single die, and success would be a five deck, and success would be picking a spades card. If anyº game. What is the probability of winning? me, you perform three tasks. You flip a quarter, and success would be and success would be a five or six. You pick a card from a full playing-card o be picking a spades card. If any of these task are successful, then you win the What do I know? What do I want to find out?

Answer 1

Problem 3 :

What do i know :

bag 1 :

P(bag 1) = 1/2

P(red | bag 1) = 3/10

P(black | bag 1) = 7/10

bag 2 :

P(bag 2) = 1/2

P(red | bag 2) = 4/10

P(black | bag 2) = 6/10

what do i want to find out :

P(bag 2 | red)

What do we expect answer to be :

answer sould be 4/7

as there are 4 red balls in bag2 and total red balls are 7

how do i go from what i know to what i want to find :

P(red) = P(red | bag 1)*P(bag 1) + P(red | bag 2)*P(bag 2)

P(red) = 3/10 * 1/2 + 4/10 * 1/2 = 7/20

P(bag 2 | red) = P(red | bag 2)*P(bag 2) / P(red)

P(bag 2 | red) = (4/10 * 1/2) / (7/20)

P(bag 2 | red) = 4/7

Yes, the answer is consistent with expected

Problem 4 :

What do i know :

P(heads) = 1/2

P(5 or 6) = 2/6 =1/3 {2 outcomes : 5, 6 is favourable out of 6 outcomes}

P(spades) = 1/4 {spades is one of the 4 suits in deck of cards}

what do i want to find out :

P(winning) = P(heads OR (5 or 6 in dice) OR spades)

P(winning) = 1 - P(not heads AND not (5 or 6 in dice) AND not spades)

P(winning) = 1 - (P(not heads)*P(not 5 or 6 in dice)*P(not spades))

P(winning) = 1 - ((1-1/2)*(1-1/3)*(1-1/4))

= 1 - (1/2)(2/3)(3/4)

= 1 - 6/24 = 1 - 1/4 = 3/4

P(winning) = 3/4

P.S. (please upvote if you find the answer satisfactory)