Answer:
1. 0.445 or 0.5
2. 0.167 or 0.2
3. Yes and No
Step-by-step explanation:
2 coins are fair and the 3rd is two-headed
So there are 2 tails and 4 heads altogether.
(A) He randomly picks one, flips it and gets a head. What is the probability that the coin is a fair one?
The probability that the coin is a fair one is: Probability of a fair coin x Probability of obtaining a head
= 2/3 x 4/6 = 0.445 to 3 decimal places
(B) He randomly picks one and flips it twice. Compute the probability that he gets 2 tails
This is = [the sum of the probability that each coin produces a tail 2 times when flipped twice] divided by 3.
For Coin 1, 0.5 is the probability of getting tails. For two consecutive tails, the probability would be 0.5 x 0.5 = 0.25
Same goes for Coin 2 which is the second fair coin.
For Coin 3, the probability of getting a tail at all is 0.
So [0.25 + 0.25 + 0] / 3 = 0.167 to 3 d.p.
(C) Suppose B = the event that the first result is head
Suppose C = the event that the second result is also head
- Are B and C independent (if the two-headed coin wasn't picked)?
YES
- Are B and C independent (if the two-headed coin was picked)?
NO
Given that Franklin has three coins, two fair coins (head on one side and tail on the other side) and one two-headed coin, to determine 1) if he randomly picks one, flips it and gets a head, what is the probability that the coin is a fair one; 2) if he randomly picks one, and flips it twice, what is the probability that he gets two tails; and 3) if he randomly picks one and flips it twice, supposing B stands for the event that the first result is head, and C represents the event that the second result is also head, if B and C are independent, the following calculations must be made:
1)
The probability that the coin is a fair one is 50%.
2)
The probability that he gets two tails is 11.11%.
3)
B and C will be independent as long as it is a fair coin.
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