Probability

Audi SG

Cards are drawn at random and without replacement from a deck of 20 cards, which are numbered 1,2,3... 20.

Events A and B are defined as follows

A - the first card drawn is less than or equal to 5

B - the seoncd card drawin is greater than or equal to 5

Find

P(B), P(A intersect B), and P(B|A)

I tried this question... for P(B), I got a value so small that it's impossible that I got the correct answer. I did this 4/20 X 16/19, considering that the FIRST card drawn is LESS than 5 and the second card can be 5 or more than 5... Can someone help me develop the chain of thoughts needed in solving this? Thanks.

wee_ws SG

Hi,

It is useful to draw a tree diagram to systematically list the possibilities. Thanks.

Cheers,
Wen Shih

Audi SG

Hi,

It is useful to draw a tree diagram to systematically list the possibilities. Thanks.

Cheers,
Wen Shih

Hi there, I have tried doing a tree diagram. However, event A and B have a common event... the card having a '5'? I am really unsure how to include that.

Thanks and I apologize for taking a while to get back to this thread

wee_ws SG

Hi,

You have identified 1st card <= 4 and 2nd card >= 5.

How about 1st card >= 5 and 2nd card > 5?

Thus we could develop the tree (with two levels and two branches per level) as follows:

1. First card level with two branches give <= 4 and >= 5.

2. If we consider the branch with <= 4, second card level with two branches lead to >= 5 and <= 4.

3. If we consider the branch with >= 5, second card level with two branches lead to >= 6 and <= 4.

Thanks.

Cheers,
Wen Shih

Andy leo2000 SG

P(B) = 76/95
P(A intersect B) = 79/380
P(B|A) = 79/95

Audi SG

P(B) = 76/95
P(A intersect B) = 79/380
P(B|A) = 79/95

Thank you :)

Andy leo2000 SG

Thank you :)

You're welcome. Probability is fun and I need to use them in my daily job :-)