17 students said they enjoy summer the most. 4 of the girls said they enjoy winter.

The ratio between boys and girls is 8 : 11.

The probability of picking a student at random who enjoys Summer is 38

Twice as many of the girls chose summer over spring.

7 boys chose summer.

Autumn was chosen by 3 more boys than girls.

The probability of picking a boy at random who chose spring is 18.75%

I attached the filled out table.

We can immediately fill out the girl/winter slot and boy/summer spot.

Knowing that there are 17 total summer lovers and 7 boy/summer, we know 10 girls love summer.

Twice as many girls picked summer than spring, so 10/2 is 5 girls picking spring.

The last clue reads weird, but says that if you pick a spring lover, there is an 18.75% chance of it being a boy, so x/(x+5)=0.1875 x=1.

38% of interviewed students preferred summer, so: 17/x = 0.38 Total students= 45

Now the annoying part:

We know that for every 8 guys, there are 11 girls.

So if we fiddle around with scaling that ratio to find the combination the adds up to 45, we get a scale of 2.35.

2.35*8=19 and 2.35*11=26

So the total number of girls is 26, meaning the number of girl/autumn is 26-5-4-10=7

Three more boys chose autumn than the girls, so 10 boy/autumn.

Total boys is 19, 1 spring, 7 summer, and 10 autumn leaves 1 to pick winter.

Good lord that took me too long to do.

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