A man possesses five coins, two of which are double-headed, one is double-tailed, and two are normal. he shuts his eyes, picks a coin at random, and tosses it. (a) what is the probability that the lower face of the coin is a head? (b) he opens his eyes and sees that the coin is showing heads. what is the probability that the lower face of the coin is a head? (c) he shuts his eyes and tosses the same coin again. what is the probability that the lower face of the coin is a head? (d) opening his eyes, the man sees that the coin is showing heads. what is the probability that the lower face of the coin is a head?
Answers
This is a question on probability.
The number of heads is :
2 × 2 = 4 heads for the coins with double heads.
The coins having a head and a tail are 2 therefore the number of heads is 2 heads.
The total number of heads is thus : 6 heads
For the tails we have :
1 double tailed = 2 tails
A tail and a head (2 coins) = 2 coins.
Total is thus 4 coins
The probability of getting a head is :
6/10
The probability of getting a tail is 4/10
The probability of getting a:
Double head coin = 2/5
Double tailed coin = 1/5
A tail and head coin = 2/5
a) The probability that the lower face is a head is :
P(the upper side is a head) and P (the coin is double headed) or P (The upper face is a tail) and P(the coin is a tail and head coin)
This equals to :
6/10 × 2/5 + 4/10 × 2/5
12/50 + 8/50 = 20/50
= 2/5
b)The probability that the lower face is a head given that it is showing heads is.
6/10 × 2/5 = 12/50
= 6/25
c) The probability that the lower face is a head is 1 since we already see that the coin is double headed meaning whichever face will face down is a head.
d) The probability is still given that we already know the outcome.