My answer is 7/8.anju wrote:-- John wrote a phone number on a note that was later lost. John can remember that the number had 7 digits, the digit 1 appeared in the last three places and 0 did not appear at all. What is the probability that the phone number contains at least two prime digits?
a) 15/16
b) 11/16
c) 11/12
d) ½
e) 5/8
You almost got it. There are 4 ways in which one out of 4 numbers is a prime. So you need to multiply 1/16 with 4parallel_chase wrote:My answer is 7/8.anju wrote:-- John wrote a phone number on a note that was later lost. John can remember that the number had 7 digits, the digit 1 appeared in the last three places and 0 did not appear at all. What is the probability that the phone number contains at least two prime digits?
a) 15/16
b) 11/16
c) 11/12
d) ½
e) 5/8
7 digits, last 3 are 1, 0 is not included.
Therefore we only have to consider 4 digits.
each digit can be filled with 8 letters (2,3,4,5,6,7,8,9)
4 prime numbers and 4 non prime numbers
probability of exactly 1 prime
probability of picking non prime letter for first digit is 1/2
probability of picking non prime letter for second digit is 1/2
probability of picking non prime letter for third digit is 1/2
probability of picking prime letter for fourth digit is 1/2
1/2*1/2*1/2*1/2 = 1/16
Similarly, probability of exactly 0 prime
will be 1/2*1/2*1/2*1/2 = 1/16
1-1/16+1/16 = probability of at least 2 prime
1/16 + 1/16 = 2/16
1-2/16 = 14/16 = 7/8
I dont know where I am going wrong. Whats the source.
Thanks !!! I feel like i just missed it.You almost got it. There are 4 ways in which one out of 4 numbers is a prime. So you need to multiply 1/16 with 4
probability one prime + probability of no primes = 4 * 1/16 + 1/16 = 5/16
probability of atleast two primes = 1 - 5/16 = 11/16 (B)
- - - - - - - 7 places . Last 3 was occupied by 1.anju wrote:-- John wrote a phone number on a note that was later lost. John can remember that the number had 7 digits, the digit 1 appeared in the last three places and 0 did not appear at all. What is the probability that the phone number contains at least two prime digits?
a) 15/16
b) 11/16
c) 11/12
d) ½
e) 5/8
Maybe I'm missing something - why don't we also consider 1 as a possible digit for the remaining numbers? The question doesn't say that 1 appears in only the last 3 digits.parallel_chase wrote:My answer is 7/8.anju wrote:-- John wrote a phone number on a note that was later lost. John can remember that the number had 7 digits, the digit 1 appeared in the last three places and 0 did not appear at all. What is the probability that the phone number contains at least two prime digits?
a) 15/16
b) 11/16
c) 11/12
d) ½
e) 5/8
7 digits, last 3 are 1, 0 is not included.
Therefore we only have to consider 4 digits.
each digit can be filled with 8 letters (2,3,4,5,6,7,8,9)
Very good thinking. Hats off! 8)bourne159 wrote:You almost got it. There are 4 ways in which one out of 4 numbers is a prime. So you need to multiply 1/16 with 4parallel_chase wrote:My answer is 7/8.anju wrote:-- John wrote a phone number on a note that was later lost. John can remember that the number had 7 digits, the digit 1 appeared in the last three places and 0 did not appear at all. What is the probability that the phone number contains at least two prime digits?
a) 15/16
b) 11/16
c) 11/12
d) ½
e) 5/8
7 digits, last 3 are 1, 0 is not included.
Therefore we only have to consider 4 digits.
each digit can be filled with 8 letters (2,3,4,5,6,7,8,9)
4 prime numbers and 4 non prime numbers
probability of exactly 1 prime
probability of picking non prime letter for first digit is 1/2
probability of picking non prime letter for second digit is 1/2
probability of picking non prime letter for third digit is 1/2
probability of picking prime letter for fourth digit is 1/2
1/2*1/2*1/2*1/2 = 1/16
Similarly, probability of exactly 0 prime
will be 1/2*1/2*1/2*1/2 = 1/16
1-1/16+1/16 = probability of at least 2 prime
1/16 + 1/16 = 2/16
1-2/16 = 14/16 = 7/8
I dont know where I am going wrong. Whats the source.
probability one prime + probability of no primes = 4 * 1/16 + 1/16 = 5/16
probability of atleast two primes = 1 - 5/16 = 11/16 (B)
We know that the single-digit numbers that are primes are 2, 3, 5, and 7.anju wrote:-- John wrote a phone number on a note that was later lost. John can remember that the number had 7 digits, the digit 1 appeared in the last three places and 0 did not appear at all. What is the probability that the phone number contains at least two prime digits?
a) 15/16
b) 11/16
c) 11/12
d) �
e) 5/8
