Question

Find the probability of selecting none of the correct six integers in a lottery, where the order in which these integers are selected does not matter, from the positive integers not exceeding the given integers.

Answer 1

Complete Questions:

Find the probability of selecting none of the correct six integers in a lottery, where the order in which these integers are selected does not matter, from the positive integers not exceeding the given integers.

a. 40

b. 48

c. 56

d. 64

Answer:

a. 0.35

b. 0.43

c. 0.49

d. 0.54

Step-by-step explanation:

(a)

The objective is to find the probability of selecting none of the correct six integers from the positive integers not exceeding 40.  

Let s be the sample space of all integer not exceeding 40.

The total number of ways to select 6 numbers from 40 is $|S| = C(40,6)$.

Let E be the event of selecting none of the correct six integers.

The total number of ways to select the 6 incorrect numbers from 34 numbers is:

$|E| = C(34,6)$

Thus, the probability of selecting none of the correct six integers, when the order in which they are selected does rot matter is  

$P(E) = \frac{|E|}{|S|}$

         $= \frac{C(34, 6)}{C(40, 6)}\\\\= \frac{1344904}{3838380}\\\\=0.35$

Therefore, the probability is 0.35

Check the attached files for additionals