Sophia has 38 Xbox and PlayStation video games. The number of Xbox games is 10 less than 5 times the number of PlayStation games How many of each type of game does she have?

X box:  30 units

PlayStation: 8 units

Step-by-step explanation:

x + p = 38

x = 5p - 10

x = number of X-Box

p = number of Play Station

then:

(5p-10) + p = 38

5p + p = 38 + 10

6p = 48

p = 48/6

p = 8

x = 5p - 10

x = 5*8  - 10

x = 40 - 10

x = 30

Check:

30 + 8 = 38

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