Coins in a box: aa conditional probability problem

In summary, the conversation discussed a question from Rice's Mathematical Statistics and Data Analysis regarding the probability of choosing a two-headed coin after flipping it twice and getting heads both times. The solution involved using conditional probability and resulted in a probability of 4/5. The individual asking the question confirmed that the solution appeared to be correct.
  • #1
Catchfire
30
0
Hello,
I've been working on some questions from Rice's Mathematical Statistics and Data Analysis and I'm not sure about my solutions.

The question I'm working on is as follows:
1.8 #59c
A box has 3 coins: 1 with two heads, 1 with 2 tails and 1 fair coin. A coin chosen randomly is flipped and comes up heads. If the coin is flipped again and comes up heads, what's the probability it's the two headed coin?

My solution:
Let A be the event the coin has two heads and let B be the event that heads is flipped twice.
P(A|B) = P(A[itex]\cap[/itex]B) / P(B) = P(B|A)P(A) / P(B) = 1*(1/3) / P(B)

P(B) = 1/3*1 + 1/3*1/4 = 5/12

P(A|B) = 1/3 / 5/12 = 4/5

Is this correct?
 
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  • #2
It looks right to me.
 
  • Like
Likes 1 person
  • #3
Thanks.

Ps sorry mods, posted in wrong forum, please move to homework subforum.
 

What is conditional probability?

Conditional probability is the likelihood of an event occurring given that another event has already occurred. It is calculated by dividing the probability of both events happening by the probability of the first event happening.

What is the "Coins in a box" problem?

The "Coins in a box" problem is a conditional probability problem where there are two boxes, one with 3 gold coins and 1 silver coin, and one with 2 gold coins and 2 silver coins. A coin is randomly chosen from one of the boxes and without looking at it, placed in the other box. Then, a coin is randomly chosen from the second box. The problem asks, what is the probability that the second coin is gold?

How do you solve the "Coins in a box" problem?

The "Coins in a box" problem can be solved by breaking it down into smaller probabilities. First, calculate the probability of choosing a gold coin from the first box. Then, calculate the probability of choosing a gold coin from the second box given that a gold coin was placed in it. Finally, use the formula for conditional probability to calculate the overall probability that the second coin is gold.

What is the formula for conditional probability?

The formula for conditional probability is P(A|B) = P(A and B)/P(B), where P(A|B) is the probability of event A occurring given that event B has occurred, P(A and B) is the probability of both events occurring, and P(B) is the probability of event B occurring.

Why is the "Coins in a box" problem important?

The "Coins in a box" problem is important because it demonstrates the concept of conditional probability, which is used in many real-world situations. It also helps to develop critical thinking and problem-solving skills, which are essential for a scientist.

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