A jar contains 99% fair coins, and 1% double-headed coins. you took a coin at random, then toss it 3 times and observed 3 heads.
2 answers:
The probability of getting 3 heads in 3 tosses of a fair coin is:
The probability of selecting a fair coin and getting 3 heads in 3 tosses is:
The probability of selecting a double-headed coin and getting 3 heads in 3 tosses is:
The probability of selecting a coin and getting 3 heads in 3 tosses is:
0.12375 + 0.01 = 0.13375
The probability that a double-headed coin was picked is:
0.01/0.13375 = 0.0748
The answer is 0.0748 or 7.48%
The probability of selecting a fair coin and getting 3 heads in 3 tosses is:
The probability of selecting a double-headed coin and getting 3 heads in 3 tosses is:
The probability of selecting a coin and getting 3 heads in 3 tosses is:
0.12375 + 0.01 = 0.13375
The probability that a double-headed coin was picked is:
0.01/0.13375 = 0.0748
The answer is 0.0748 or 7.48%
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There are 100 numbers in the range 100-199. Find the smallest and largest multiple of 13 in this range. We have
104 = 8•13
195 = 15•13
so there are 15 - 8 + 1 = 8 multiples of 13 between 100 and 199.
Then the sum we want is
or equivalently,
(100 + 101 + 102 + … + 199) - 13 (8 + 9 + … + 15)
To compute these sums, recall the following formula:
Then
and
which means the sum we want is 14,950 - 1,196 = 13,754.