Answer:
Given that your friend in not really psychic, he has a probability of P=1.5% of guessing right 15 out of 20 coin flips.
Step-by-step explanation:
We have a binomial distribution problem.
We have to calculate the probability of correctly guessing 15 out of 20 flips of a coin (probability of success for every trial: p=0.5).
We can calculate that with the binomial distribution formula:
![P(x)=\frac{n!}{x!(n-x)!}p^x(1-p)^{n-x} \\\\P(15)=\frac{20!}{15!*5!}0.5^{15}*0.5^5\\\\P(15)=15504*0.5^{20}=15504* 0.00000095367 = 0.015](https://tex.z-dn.net/?f=P%28x%29%3D%5Cfrac%7Bn%21%7D%7Bx%21%28n-x%29%21%7Dp%5Ex%281-p%29%5E%7Bn-x%7D%20%5C%5C%5C%5CP%2815%29%3D%5Cfrac%7B20%21%7D%7B15%21%2A5%21%7D0.5%5E%7B15%7D%2A0.5%5E5%5C%5C%5C%5CP%2815%29%3D15504%2A0.5%5E%7B20%7D%3D15504%2A%200.00000095367%20%3D%200.015)
Then we can conclude that, given that your friend in not really psychic, it has only 1.5% of guessing right 15 out of 20 coin flips.
The formula of a slope:
![m=\dfrac{y_2-y_1}{x_2-x_1}](https://tex.z-dn.net/?f=m%3D%5Cdfrac%7By_2-y_1%7D%7Bx_2-x_1%7D)
We have the points (4, -4) and (k, -1) and the slope m = 34.
Substitute:
![\dfrac{-1-(-4)}{k-4}=34\\\\\dfrac{3}{k-4}=\dfrac{34}{1}\qquad|\text{cross multiply}\\\\34(k-4)=3\qquad|\text{use distributive property}\\\\34k-136=3\qquad|+136\\\\34k=139\qquad|:34\\\\k=\dfrac{139}{34}](https://tex.z-dn.net/?f=%5Cdfrac%7B-1-%28-4%29%7D%7Bk-4%7D%3D34%5C%5C%5C%5C%5Cdfrac%7B3%7D%7Bk-4%7D%3D%5Cdfrac%7B34%7D%7B1%7D%5Cqquad%7C%5Ctext%7Bcross%20multiply%7D%5C%5C%5C%5C34%28k-4%29%3D3%5Cqquad%7C%5Ctext%7Buse%20distributive%20property%7D%5C%5C%5C%5C34k-136%3D3%5Cqquad%7C%2B136%5C%5C%5C%5C34k%3D139%5Cqquad%7C%3A34%5C%5C%5C%5Ck%3D%5Cdfrac%7B139%7D%7B34%7D)
Answer:
The answer to 1 1/2 + 1/6 is 1 2/3.