Omar has four times as many apples as bananas he has 30 pieces of fruit in all of a represents the number of apples and b represents the number of bananas, how many of each fruit does omar have ?

24 apples and 6 bananas.

Step-by-step explanation:

Omar has 4 times as many apples as bananas; this means if is the number of apples, and is the number of bananas

    1.

The total pieces of fruit is 30; this means

   2.

Thus we have two equations, and we solve them by substituting for   in equation (2) with from equation (1):

Omar has 6 bananas.

Now we substitute  this into equation(1) and get:

Omar has 24 apples.

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