11.3 - Independent and Dependent Events

11.3 - Independent and Dependent Events

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Independent Events

• The occurrence of one event does not affect the probability of another

• If A and B are independent events, then P(A and B) = P(A) * P(B)

Example

• A coin is flipped three times. What is the probability it lands heads all three times?

• The outcome of any flip does not affect the next one, so the events are independent.

• Multiply the probabilities.

•  $\frac{1}{2}\cdot\frac{1}{2}\cdot\frac{1}{2}=\frac{1}{8}$  

You try

Open Ended

When rolling two dice, what is the probability of rolling a 7 and then rolling an 11?

Dependent Events

• The occurrence of one event affects the probability of the other

• If A and B are dependent events, then P(A and B) = P(A) * P(B | A), where P(B | A) is the probability of B, given that A has already occurred.

Example

• A standard deck of playing cards has 52 cards made up of 4 suits (diamonds, hearts, clubs, spades) of 13 cards each.

• You select a diamond from the deck and do not replace it. What is the probability that you select another diamond with your next draw?

• Multiply the probabilities

•  $\frac{13}{52}\cdot\frac{12}{51}=\frac{1}{4}\cdot\frac{4}{17}=\frac{1}{17}$  

Hint

Look for the words "with replacement" (independent events) or "without replacement" (dependent events) to help you determine whether events are independent or dependent.

Multiple Choice

Which describes dependent events?

• Flipping a fair coin three times.

• Drawing a card from a deck, replacing it, and then drawing another card.

• Playing the game of Concentration, turning over a card then turning over another card hoping for a pair.

• Rolling a pair of dice. The first roll is an 8. The second roll is an odd number.

Multiple Choice

A bag contains 10 beads (2 black, 5 red, 3 white). Determine the probability of selecting a white bead, replacing it, then selecting a red bead.

• $\frac{3}{10}\cdot\frac{5}{9}=\frac{15}{90}=\frac{1}{6}$

• $\frac{3}{10}\cdot\frac{5}{10}=\frac{15}{100}=\frac{3}{20}$

• $\frac{2}{10}\cdot\frac{5}{10}=\frac{10}{100}=\frac{1}{10}$

• $\frac{3}{10}\cdot\frac{2}{10}=\frac{6}{100}=\frac{3}{50}$

Multiple Choice

Ten cards numbered 1-10 are placed in a hat. What is the probability of randomly drawing a card with an even number then a card with a number greater than or equal to five if the first card is replaced?

• 1/4
• 2/3
• 3/10
• 3/5

Multiple Choice

Lisa flipped the same coin 3 times. What is the probability she obtained all tails?

• 1/2

• 1/4

• 1/16

• 1/8

Multiple Choice

A jar contains 4 white chips, 5 purple chips, and 1 black chip. Chips are selected randomly one at a time, and are not replaced. P(purple then black)

• 1/18

• 2/5

• 3/7

• 4/9