1. Conditional probabilities start at their condition.
2. Nonconditional probabilities start at the beginning of the tree.
3. Multiply when moving horizontally across a limb.
4. Add when moving vertically from limb to limb.

Possible Classroom Examples:

• In a newspaper poll concerning violence on television, 600 people were asked, "What is your opinion of the amount of violence on prime-time television -- is there too much violence on television?". Their responses are summarized in the table below.

	Yes	No	Don't Know	Total
Men	162	95	23	280
Women	256	45	19	320
Total	418	140	42	600

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• Cards are dealt from a full deck of 52. Find the probability of each of the given events.
• the first card is a diamond
• the second card is a spade, given that the first card was a diamond
• the first card is a diamond and the second card is a spade
• draw a tree diagram illustrating this

• Five cards are dealt from a full deck. Find the probability that the last four are spades, given that the first was a spade.

• A personal computer manufacturer buys 38% of its chips from Japan and the rest from America. 1.7% of the Japanese chips are defective, and 1.1% of the American chips are defective.
• Find the probability that a chip is defective and made in Japan.
• Find the probability that a chip is defective and made in America.
• Find the probability that a chip is defective.
• Find the probability that a chip is defect-free.

© 2007 Elizabeth E. K. Jones and the ASU Department of Mathematics and Statistics - All rights reserved.