The mean age of 5 people in a room is 40 years. A person enters the room. The mean age is now 40. What is the age of the person who entered the room?

40

Step-by-step explanation:

5 people in the room have  5*40 = 200 years altogether

a new person is X years old.

Now 6 people have (200 + x) years altogether.

Mean age of 6 people  is (200+x)/6. and it is also = 40.

So,

(200+x)/6 = 40

200 + x = 240

x = 40

85.560%

step-by-step explanation:

conditional probability is defined as:

p(a|b) = p(a∩b) / p(b)

in other words, the probability that a occurs, given that b has occurred = the probability that both a and b occur / the probability that b occurs.

in this example:

p(turns 64 | turns 44) = p(turns 64 & turns 44) / p(turns 44).

if someone turns 64, they must have already turned 44, so:

p(turns 64 | turns 44) = p(turns 64) / p(turns 44)

on page 42, we see that of the original 100,000, 94944 turn 44, and 81234 turn 64.   therefore:

p(turns 64 | turns 44) = 81234 / 94944

p(turns 64 | turns 44) = 0.85560