Answer:
a) a combination
b) The probability = 1 ÷ [ Number of ways to select the four dancers ]
Step-by-step explanation:
a) Here it is only required to calculate the number of ways to select the four dancers and the order of the dancers is not required i.e not important for us.
Hence, we will use a combination to select 4 out of 22 dancers
i.e ²²C₄
b) Since the dancers selected are 4 predetermined individuals
therefore,
number of ways to select selecting dancers Laura, Matthew, Lakiesha, and Santos will be '1'
Hence,
The probability = 1 ÷ [ Number of ways to select the four dancers ]
= 1 ÷ ²²C₄
Answer: 0.5898
Step-by-step explanation:
Given : J.J. Redick of the Los Angeles Clippers had a free throw shooting percentage of 0.901 .
We assume that,
The probability that .J. Redick makes any given free throw =0.901 (1)
Free throws are independent.
So it is a binomial distribution .
Using binomial probability formula, the probability of getting success in x trials :

, where n= total trials
p= probability of getting in each trial.
Let x be binomial variable that represents the number of a=makes.
n= 14
p= 0.901 (from (1))
The probability that he makes at least 13 of them will be :-

![=^{14}C_{13}(0.901)^{13}(1-0.901)^1+^{14}C_{14}(0.901)^{14}(1-0.901)^0\\\\=(14)(0.901)^{13}(0.099)+(1)(0.901)^{14}\ \ [\because\ ^nC_n=1\ \&\ ^nC_{n-1}=n ]\\\\\approx0.3574+0.2324=0.5898](https://tex.z-dn.net/?f=%3D%5E%7B14%7DC_%7B13%7D%280.901%29%5E%7B13%7D%281-0.901%29%5E1%2B%5E%7B14%7DC_%7B14%7D%280.901%29%5E%7B14%7D%281-0.901%29%5E0%5C%5C%5C%5C%3D%2814%29%280.901%29%5E%7B13%7D%280.099%29%2B%281%29%280.901%29%5E%7B14%7D%5C%20%5C%20%5B%5Cbecause%5C%20%5EnC_n%3D1%5C%20%5C%26%5C%20%5EnC_%7Bn-1%7D%3Dn%20%5D%5C%5C%5C%5C%5Capprox0.3574%2B0.2324%3D0.5898)
∴ The required probability = 0.5898
The answer is 42 because 42 times 1 equals 42, 2 times 21 equals 42 and 3 times 14 equals 42.
The standard form is pretty much the variables on the left-hand-side and the constant alone by herself on the right-hand-side, with only positive integers on the x-variable and an integers all around.