Question

In a fiftness class, there was a warm up of 14 press-ups. Anyone unable to do 14 or more recives a punishment. Jessica can do 10 press-ups without ever failing, however, the chances of her successfully doing each subsequent press-up halves. Whats the probality of her receiving a punishment? A. 1 in 8 B. 1 in 1024 C. 15 in 16 D. 1023 in 1024

Answer 1

The correct option is;

C. 15 in 16

Explanation:

The given information are;

The number of press-ups required = 14 press-ups

The number of press-ups Jessica is sure to do = 10 press-ups

The chance of Jessica doing subsequent press-ups after 10 halves each time

The consequence of not completing the 14 press-ups = Punishment

The probability that Jessica does goes on to do 11 press-ups = 1/2

The probability that Jessica does goes on to do 12 press-ups = 1/2×1/2

The probability that Jessica does goes on to do 13 press-ups = 1/2×1/2×1/2

The probability that Jessica does goes on to do (completes) 14 press-ups = 1/2×1/2×1/2×1/2 = 1/16

Therefore;

Since the probability that Jessica does not receive a punishment because she completed the 14 push-ups is 1/16, we have;

The probability that Jessica does not complete the 14 press-ups and receives a punishment = 1 - 1/16 = 15/16 which is 15 times out of 16 or 15 in 16.