Question

I have a collection of baseball cards, some from the 1984 season and some from other seasons. Considering only my valuable baseball cards, 60% of them are from 1984. Overall, 3% of my baseball cards are both valuable and from the 1984 season, and 38% of my cards are not valuable and not from the 1984 season. Fill out the table below

p(1984 and V) =

p(not 1984 and V) =

p(V) =

p(1984 and not V) =

p(not 1984 and not V) =

p(not V) =

p(1984) =

p(not 1984) =

Answer 1

We are given that "considering only valuable cards, 60% of them are from 1984" which can be written as:
P(1984|V) = 0.60 ....................(1)

Also, we are given that "3% of the cards are both valuable and from 1984 season" which can be written as:

P(1984 V) = 0.03 .....................(2)

Also, we are given that "38% of cards are not valuable and not from 1984 season" which can be written as:

P(V^c 1984^c) = 0.38 .......................(3)

Before we move on to finding the answers to the required probabilities, we find the probabilites P(1984), P(V) and

P(1984V) which are the basic probabilities and can be used to answer all the parts.

From equation (1), we get:

From equation (3), we get:

Part (a)

Part (b)

Part (c)

P(V) = 0.05 [Answer] [Using equation (4)]

Part (d)

Part (e)

Part (f)

Part (g)

P(1984) = 0.60 [Answer] [Using equation (6)]

Part (h)

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