7.4 Probability of Independent Events

4/17/2013

2. What is the number of unique 4-digit ATM PINcodes if the first number cannot be 0?

The numbers to choose from are 0, 1, 2, 3, 4, 5, 6, 7, 8 or 9

1st digit 2nd digit 3rd digit

9 10 10● ● 10●4th digit

Since 0 can’t be the 1st number

= 9000

Probabilitya way to measure the chance that an event will occur

a fraction, a percent or decimal.

Definition:

Formula:

How it is written:

You roll a 6-sided die whose sides are numbered 1 through 6. Find the probability of a.) rolling a 4 b.) rolling an odd number and c.) rolling a number less than 5.a. Rolling a 4.Number of ways it can happen: 1 since there’s only 1 way of rolling a 4Number of possible outcomes: 6P = or .1 or 16. %b. Rolling an odd number.Number of ways it can happen : 3 since you can roll a 1, 3 or 5.Number of possible outcomes: 6P = or .5 or 50 %

You roll a 6-sided die whose sides are numbered 1 through 6. Find the probability of a.) rolling a 4 b.) rolling an odd number and c.) rolling a number less than 5.a. Rolling a number less than 5.Number of ways it can happen : 4 since you can roll a 1, 2, 3 or 4.Number of possible outcomes: 6P = or . or 66. %

14. At the time of your turn, a particular Scrabble bag contains 5 Es, 3 Rs, 4 Os, and 5 As. What is the probability that you will pull an R?

The bag contains 5+3+4+5 = 17 lettersNumber of ways it can happen: 3 RsNumber of possible outcomes: 17

𝑃=317 ≈ .176

A bag of marbles contains 9 large green marbles, 4 large purple marbles, 5 small green marbles, and 4 small yellow marbles. If you draw a marble at random, what is the probability that you will draw a green marble, given that it is large?

The bag contains 9+4 = 13 LARGE marblesNumber of ways it can happen : 9 LGNumber of possible outcomes: 13

.692

2 or more events that do not have an effect on the outcomes of each event .

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

Probability of A and B occuring.

Definition:

Probability of Independent Events:

Independent Events

Multiply the probability of each event.

You flip a coin four times where one side is heads and the other side is tails. What is the chance that you will flip heads the first two times and tails the second two times.

Number of ways it can happen : 1Number of possible outcomes: 16

P =

P(H in 1st toss) = P(H in 2nd toss) = P(T in 3rd toss) = P(T in 4th toss) = P(HHTT) =

Or Use P(A and B) = P(A) •P(B)

18. A jar contains 20 red M&Ms, 23 yellow M&Ms, 19 green M&Ms, 15 blue M&Ms, and 17 brown M&Ms. What is the probability of pulling a yellow M&M, replace it in the jar, and then pulling a green M&M?The jar contains 20+23+19+15+17 = 94 M&MsNumber of ways it can happen : 23 Yellow M&MsNumber of ways it can happen : 19 Green M&MsNumber of possible outcomes: 94

𝑃 (𝑌𝐺 )=2394 ∙1994=

4378836 ≈ .049≈5%

A random number generator selects three digits from {0, 1, …, 9}. What is the probability that all three numbers are less than or equal to 4?Numbers less than or equal to 4: 0, 1, 2, 3, 4Number of ways it can happen : 5Number of possible outcomes: 10 (0, 1, 2, 3, 4, 5, 6, 7, 8, 9)

The official weather forecast calls for a 30% chance of rain Saturday, a 40% chance rain Sunday, and a 50% chance rain Monday. What is the probability that it DOES NOT rain on any of those days?

Homework

WS 7.4Odd problems only