Probability of Coins and Outcomes

The video tutorial explains a probability problem involving eight coins, three of which are unfair with a 60% chance of heads, while the rest are fair with a 50% chance. The task is to find the probability of getting two heads when a coin is randomly selected and flipped twice. The solution involves visualizing the problem with a decision tree, calculating probabilities for both fair and unfair coins, and summing these probabilities to find the total probability of getting two heads. The final probability is approximately 29.13%.

How many coins in the bag are unfair?

• Three

• Five

• Eight

• Two

What is the probability of getting heads with a fair coin?

• 60%

• 50%

• 70%

• 40%

What method is used to solve the problem of finding the probability of two heads?

• Simulation

• Algebraic equation

• Decision tree

• Graphical analysis

What is the probability of picking a fair coin from the bag?

• 1/2

• 1/4

• 3/8

• 5/8

What is the probability of getting two heads in a row with a fair coin?

• 25%

• 100%

• 50%

• 75%

What is the probability of getting two heads in a row with an unfair coin?

• 60%

• 50%

• 25%

• 36%

What is the probability of picking an unfair coin from the bag?

• 1/2

• 5/8

• 1/4

• 3/8

What is the combined probability of getting two heads in a row, considering both fair and unfair coins?

• 29.13%

• 50%

• 25%

• 36%

Why is the overall probability of getting two heads higher than 25%?

• Because there are more fair coins

• Because unfair coins have a higher chance of heads

• Because all coins are fair

• Because the bag is biased

If all coins were fair, what would be the probability of getting two heads in a row?

• 36%

• 50%

• 25%

• 29.13%