From each of the lists above, one number is selected at random and the

Question

A = {7, 9, 15, 20}
B = {4, 5, 6, 11}

From each of the lists above, one number is selected at random and these two numbers comprise list C. What is the probability that list C contains one number less than 10 and another number greater than 10 ?

A 3/16
B. 3/8
C. 7/16
D. 1/2
E. 5/8

The sets S1={15,9,20,7} and S2= {6,11,5,4} both have one or more numbers over 10. If one number from S1 and one number from S2 are selected randomly, what is the probability that the set selected will have one number over 10 and one number under 10?

PyjamaScientist · Answer

Probability that list C contains one number less than 10 and another number greater than 10:

Since we are picking one no. from each set, only two cases are possible.

Case 1: smaller than 10 no. comes from A and greater than comes from B.
Thus, probability of <10 no. coming from A = \(1/2\), and probability of >10 no. coming from B = \(1/4\).
Total probability for case 1 = \(1/8\).

Similarly for Case 2: smaller than 10 no. comes from B and greater than comes from A.
Thus, probability of <10 no. coming from B = \(3/4\), and probability of >10 no. coming from A = \(1/2\).
Total probability for case 2 = \(3/8\).

Complete total probability = \(1/8 + 3/8 = 1/2\). Option (D).

Adarsh_24 · Answer

Alternative approach

A:
Lesser than 10(L)=2
Greater(G)=2

B:
L=3
G=1

(2c1*1c1+2c1*3c1)/(4c1*4c1)=1/2

shamid19 · Answer

I go manually through the list - start with 7,4 wrong, 7,5 wrong, 7,6 wrong, 7,11 correct. I'll do it with the other numbers as well and then count the number of "success" over the "total" number. Is there a more intuitive and faster way to solve this question?

Bunuel · Answer

Official Solution:

A = {7, 9, 15, 20}
 
B = {4, 5, 6, 11}
 
One number is randomly selected from each of the lists above to form list C. What is the probability that list C contains one number less than 10 and the other greater than 10?

A.  \frac{3}{16} 
B.  \frac{3}{8} 
C.  \frac{7}{16} 
D.  \frac{1}{2} 
E.  \frac{5}{8}

The probability that the number selected from List A is less than 10 and the number from List B is greater than 10 is  \frac{1}{2} * \frac{1}{4} = \frac{1}{8} .

The probability that the number selected from List A is greater than 10 and the number from List B is less than 10 is  \frac{1}{2} * \frac{3}{4} = \frac{3}{8} .

Thus, the overall probability is  \frac{1}{8} + \frac{3}{8} = \frac{1}{2} .

Answer: D

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