Question

Consider an urn with 20 red balls, 30 blue balls, and 15 yellow balls, along with a standard deck of cards (jokers excluded). Consider the following events: A = {a red or blue ball is drawn}, B = {a yellow or blue ball is drawn}, C = {a heart is drawn}, D = {a face card is drawn}. Assuming you’ll draw a single ball and a single card, calculate the following.

1. p(A), p(C).

2. p(B and C), p(C and D)

3. p(A or B), p(A or D)

4. p(A|B), p(A|D)

Answer 1

Reds= 30, Blue = 20 and Yellow =15 Total =65

We have a standard deck except Jokers = 52-4=48 cards

A = {a red or blue ball is drawn},

B = {a yellow or blue ball is drawn},

C = {a heart is drawn},

We have 4 hearts in the deck of 48 cards here.

D = {a face card is drawn}.

A face card means a king or queen or joker.

Joker is not in the deck.

So

1)

P(A)=10/13, P(C)=1/12

2)

p(B and C),

p(C and D)

C and D have no card in common so P(C and D )=0

3)

4.

We have 30 blue balls which are common in both A and B

No intersection between card and ball.