Probability: Independent and Dependent Events

Probability: Independent and Dependent Events

Independent & Dependent Events

• Independent - One activity does NOT effect the outcome of a different activity. (REPLACE)

• Dependent - One activity DOES effect the outcome of another activity. (do NOT replace)

Multiple Choice

You roll a number cube twice. The first time is a 3 and the second time is an even number.

• Independent

• Dependent

Multiple Choice

You randomly draw a marble from a bag of marbles. You get a red and don't put it back into the bag. You draw another marble out of the bag and get a yellow.

• Independent

• Dependent

Multiple Choice

Kathy draws a 4 from a set of cards numbered 1 - 10, and rolls a 2 on a number cube.

• Independent

• Dependent

Multiple Choice

Yuki chooses a book from the shelf to read, then Janette chooses a book from the books that remain.

• Independent

• Dependent

Independent Events

• To find the probability that two independent events will happen - MULTIPLY the probabilities of the two events.

Find the probability of choosing a green marble at random from a bag containing 5 green and 10 white marbles and then flipping a coin and getting tails.

•  $P\left(Green\right)=\frac{5}{15}=\frac{1}{3}$  

•  $P\left(Tails\right)=\frac{1}{2}$  

•  $P\left(Green\ and\ Tails\right)=\ \frac{1}{3}\times\frac{1}{2}=\frac{1}{6}$  

Dependent Events

You must determine the effect that the first event has on the probability of the second event.

A reading list contains 5 historical books and 3 science-fiction books. What is the probability that Juan will randomly choose a historical book for his first report and a science-fiction book for his second?

• Total # of books = 8

•  $P\left(historical\right)\ =\ \frac{5}{8}$  

•  $P\left(science-fiction\right)\ =\ \frac{3}{7}$  

•  $P\left(historical\ then\ Sci-Fi\right)=\ \frac{5}{8}\times\frac{3}{7}=\frac{15}{56}$  

Multiple Choice

Decide whether each event is independent or dependent.

Mary chooses a game piece from a board game, and then Jason chooses a game piece from the three remaining pieces.

• Independent

• Dependent

Multiple Choice

Find the probability of spinning an evenly divided spinner numbered 1-8 and getting a PRIME number on one spin and getting an ODD number on a second spin.

• $\frac{1}{2}$

• $\frac{1}{4}$

• $\frac{5}{8}$

• $\frac{3}{16}$

Multiple Choice

Sarah picks 2 hats at random from 5 bill caps and 3 beanies. What is the probability that both are bill caps?

• $\frac{5}{8}$

• $\frac{15}{64}$

• $\frac{3}{8}$

• $\frac{5}{14}$

Multiple Choice

What is the probability that Anne will choose 2 apples from a bin of 10 apples, 8 bananas, and 7 oranges?

• $\frac{2}{25}$

• $\frac{11}{25}$

• $\frac{3}{20}$

• $\frac{18}{25}$