Dependent Events

Dependent Events

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Multiple Choice

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Multiple Choice

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Multiple Choice

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Multiple Choice

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At the end of the lesson, the students will be able to:

• Find the probability of Simple Events.

• Use AND, OR, and Complements in finding probabilities of an event.

• Differentiate Independent and Dependent Events.

Dependent Event Examples

• A card is chosen at random from a standard deck of 52 playing cards. Without replacing it, a second card is chosen. What is the probability that the first card chosen is a queen and the second card chosen is a jack?

  
  

• Analysis: The probability that the first card is a queen is 4 out of 52. However, if the first card is not replaced, then the second card is chosen from only 51 cards. 

• Accordingly, the probability that the second card is a jack given that the first card is a queen is 4 out of 51.

Conclusion:

• The outcome of choosing the first card has affected the outcome of choosing the second card, making these events dependent.

Solution:

• P(queen on first pick)

   $\frac{4}{52}$  

• P(jack on 2nd pick given queen on 1st pick) $\frac{4}{51}$  

• P(queen and jack)  $\frac{4}{52}\ x\ \frac{4}{51}\ =\ \frac{16}{2652}\ =\frac{4}{663}$  

Dependent Events

• If A & B are dependent events, then the probability that both A & B occur is:

  P(A&B) = P(A) * P(B/A)

• The probability that B will occur given that A has occurred is called the conditional probability of B given A and is written P(B|A).

Comparing Dependent and Independent Events

• You randomly select two cards from a standard 52-card deck. What is the probability that the first card is not a face card (a king, queen, or jack) and the second card is a face card if:

• (1) you replace the first card before selecting the second, and

  (2) you do not replace the first card?

Comparing Dependent and Independent Events

• (1) If you replace the first card before selecting the second card, then A and B are independent events. So, the probability is:
  

   $P(AandB)=P(A)\ •\ P(B)=\frac{40}{52}x\ \frac{12}{52}\ =\ \frac{30}{169}\approx0.178$  

• (2) If you do not replace the first card before selecting the second card, then A and B are dependent events. So, the probability is:
   $P(AandB)=P(A)•P(B|A)=\frac{40}{52}x\ \frac{12}{51}\ =\ \frac{40}{221}\approx0.0181$  
  

Poll

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Multiple Choice

Is the event INDEPENDENT or DEPENDENT?

The spinner is spun twice. What is the probability that it lands on red first and then blue?

• Independent

• Dependent

Multiple Choice

Sue will randomly select from a treat bag containing 6 lollipops and 4 gum balls. Sue will select a treat, not replace it, and then select a second treat.

• Independent

• Dependent

Multiple Choice

Tom will randomly select from a treat bag containing 6 lollipops and 4 gum balls. Tom will select a treat, replace it, and then select a second treat.

• Independent

• Dependent

Multiple Choice

Cindy flips a coin once, records the result, then flips it again. Does this situation represent INDEPENDENT or DEPENDENT events?

• Independent

• Dependent

Multiple Choice

Is the event INDEPENDENT or DEPENDENT?

Amy plays card games. She picks a card at random. Then without putting the first card back, he picks a second card at random.

• Independent

• Dependent

Multiple Choice

An event is DEPENDENT, if...

• The first event has no affect on the next event

• The first event affects the second event

Open Ended

In your own words, how do you know if the probability is dependent event?

Classwork:

Independent and Dependent Events