Independent Probability L2

1. Independent Probability L2

By Henry Phan

​Independent Probability

​Two events are said to be independent of each other: the probability of one event occurs doesn’t affects the probability of the other event occurring.

Example: you rolled a die and flipped a coin.

​Independent Probability

Probability of​

• ​Rolling a die: 1/6

• Tossing a coin: 1/2

• Picking a card: 4/52​

​

​Independent Probability

Probability of​

• ​Picking two cards

• Tossing two coins

• Rolling two dice:

​Independent Probability

Probability of​

• ​Picking a card: 4/52

• Picking two cards:

​Independent Probability

Probability of​

• ​Tossing a coin: 1/2

• Rolling two coins:

​Independent Probability

Probability of​

• ​Rolling a die: 1/6

• Rolling two dice:

Multiple Choice

Determine Probability of picking a card with "two" rolling a dice on "two", and tossing a coin on "head" again on three different standard decks of cards?

P(3 of "3" cards) = ?

• $$\left(\frac{2}{2}\right)\left(\frac{2}{6}\right)\left(\frac{4}{52}\right)$$  

• $$\left(\frac{2}{2}\right)\left(\frac{2}{6}\right)\left(\frac{2}{52}\right)$$  

• $$\left(\frac{1}{2}\right)\left(\frac{1}{6}\right)\left(\frac{1}{52}\right)$$  

• $$\left(\frac{1}{2}\right)\left(\frac{1}{6}\right)\left(\frac{4}{52}\right)$$  

Multiple Choice

Determine Probability of picking three cards, a "3", another "3", and a "3" again on three different standard decks of cards?

P(3 of "3" cards) = ?

• $$\left(\frac{4}{52}\right)\left(\frac{4}{52}\right)\left(\frac{4}{52}\right)$$  

• $$\left(\frac{1}{6}\right)\left(\frac{1}{6}\right)\left(\frac{1}{6}\right)$$  

• $$\left(\frac{1}{3}\right)\left(\frac{1}{3}\right)\left(\frac{1}{3}\right)$$  

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

Multiple Choice

Determine Probability of tossing 3 coins, a head, a tail, and another head?

P(3 coins) = ? 

• $$\left(\frac{4}{52}\right)\left(\frac{4}{52}\right)\left(\frac{4}{52}\right)$$   

• $$\left(\frac{1}{6}\right)\left(\frac{1}{6}\right)\left(\frac{1}{6}\right)$$  

• $$\left(\frac{1}{3}\right)\left(\frac{1}{3}\right)\left(\frac{1}{3}\right)$$  

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

Multiple Choice

Determine Probability of rolling 3 dice, a "3", another "3", and a "3" again?

P(3 dice) = ?

• $$\left(\frac{4}{52}\right)\left(\frac{4}{52}\right)\left(\frac{4}{52}\right)$$  

• $$\left(\frac{1}{6}\right)\left(\frac{1}{6}\right)\left(\frac{1}{6}\right)$$  

• $$\left(\frac{1}{3}\right)\left(\frac{1}{3}\right)\left(\frac{1}{3}\right)$$  

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

​Independent Probability of dices

​Greater count up​

​Less count down

​Example: Dice and Greater

Roll two standard six-sided dice, what is the probability that both and on a 5 or greater

​P(die 1) =

​P(die 2) =

​P(2 dice greater) =

​Example: Dice and Greater

Roll three standard six-sided dice, what is the probability that altogether land on a 5 or greater

​P(die 1) =

​P(die 2) =

​P(die 3) =

​P(3 dice greater) =

​Example: Dice and Less

Roll two standard six-sided dice, what is the probability that both land on a 5 or less

​P(die 1) =

​P(die 2) =

​P(2 dice less) =

​Example: Dice and Less

Roll three standard six-sided dice, what is the probability that altogether land on a 5 or less

​P(die 1) =

​P(die 1) =

​P(die 1) =

​P(3 dice less) =

​Example: Dice and Greater

Roll two standard six-sided dice, what is the probability that both land on a 3 or greater

​P(die 1) =

​P(die 2) =

​P(3 dice greater) =

​Example: Dice and Less

Roll three standard six-sided dice, what is the probability that altogether land on a 3 or less

​P(die 1) =

​P(die 2) =

​P(die 3) =

​P(3 dice less) =

​Example: Dice and Greater

Roll three standard six-sided dice, what is the probability that altogether land on a 3 or greater

​P(die 1) =

​P(die 2) =

​P(die 3) =

​P(3 dice greater) =

​Example: Dice and Less

Roll three standard six-sided dice, what is the probability that altogether land on a 3 or less

​P(die 1) =

​P(die 2) =

​P(2 dice greater) =

​Example: Dice and Less

Roll three standard six-sided dice, what is the probability that altogether land on a 3 or less

​P(die 1) =

​P(die 2) =

​P(die 3) =

​P(3 dice greater) =

Multiple Choice

Roll three standard six-sided dice, what is the probability that all land on a 2 or greater

• $$\left(\frac{2}{6}\right)\left(\frac{2}{6}\right)\left(\frac{2}{6}\right)$$  

• $$\left(\frac{3}{6}\right)\left(\frac{3}{6}\right)\left(\frac{3}{6}\right)$$  

• $$\left(\frac{4}{6}\right)\left(\frac{4}{6}\right)\left(\frac{4}{6}\right)$$  

• $$\left(\frac{5}{6}\right)\left(\frac{5}{6}\right)\left(\frac{5}{6}\right)$$  

Multiple Choice

Roll three standard six-sided dice, what is the probability that all land on a 2 or less

• $$\left(\frac{2}{6}\right)\left(\frac{2}{6}\right)\left(\frac{2}{6}\right)$$  

• $$\left(\frac{3}{6}\right)\left(\frac{3}{6}\right)\left(\frac{3}{6}\right)$$  

• $$\left(\frac{4}{6}\right)\left(\frac{4}{6}\right)\left(\frac{4}{6}\right)$$  

• $$\left(\frac{5}{6}\right)\left(\frac{5}{6}\right)\left(\frac{5}{6}\right)$$  

Multiple Choice

Roll three standard six-sided dice, what is the probability that all land on a 4 or greater

• $$\left(\frac{2}{6}\right)\left(\frac{2}{6}\right)\left(\frac{2}{6}\right)$$  

• $$\left(\frac{3}{6}\right)\left(\frac{3}{6}\right)\left(\frac{3}{6}\right)$$  

• $$\left(\frac{4}{6}\right)\left(\frac{4}{6}\right)\left(\frac{4}{6}\right)$$  

• $$\left(\frac{5}{6}\right)\left(\frac{5}{6}\right)\left(\frac{5}{6}\right)$$  

Multiple Choice

Roll three standard six-sided dice, what is the probability that all land on a 4 or less

• $$\left(\frac{2}{6}\right)\left(\frac{2}{6}\right)\left(\frac{2}{6}\right)$$  

• $$\left(\frac{3}{6}\right)\left(\frac{3}{6}\right)\left(\frac{3}{6}\right)$$  

• $$\left(\frac{4}{6}\right)\left(\frac{4}{6}\right)\left(\frac{4}{6}\right)$$  

• $$\left(\frac{5}{6}\right)\left(\frac{5}{6}\right)\left(\frac{5}{6}\right)$$  

Multiple Choice

Roll four standard six-sided dice, what is the probability that all land on a 3 or less

• $$\left(\frac{2}{6}\right)\left(\frac{2}{6}\right)\left(\frac{2}{6}\right)\left(\frac{2}{6}\right)$$  

• $$\left(\frac{3}{6}\right)\left(\frac{3}{6}\right)\left(\frac{3}{6}\right)\left(\frac{3}{6}\right)$$  

• $$\left(\frac{4}{6}\right)\left(\frac{4}{6}\right)\left(\frac{4}{6}\right)\left(\frac{4}{6}\right)$$  

• $$\left(\frac{5}{6}\right)\left(\frac{5}{6}\right)\left(\frac{5}{6}\right)\left(\frac{5}{6}\right)$$  

Multiple Choice

Roll four standard six-sided dice, what is the probability that all land on a 5 or greater

• $$\left(\frac{2}{6}\right)\left(\frac{2}{6}\right)\left(\frac{2}{6}\right)\left(\frac{2}{6}\right)$$  

• $$\left(\frac{3}{6}\right)\left(\frac{3}{6}\right)\left(\frac{3}{6}\right)\left(\frac{3}{6}\right)$$  

• $$\left(\frac{4}{6}\right)\left(\frac{4}{6}\right)\left(\frac{4}{6}\right)\left(\frac{4}{6}\right)$$  

• $$\left(\frac{5}{6}\right)\left(\frac{5}{6}\right)\left(\frac{5}{6}\right)\left(\frac{5}{6}\right)$$