a computer is programmed to select two random numbers from 1 to 5. all possible outcomes are shown in the…

a computer is programmed to select two random numbers from 1 to 5. all possible outcomes are shown in the table. each outcome has equal probability.\n1,1 1,2 1,3 1,4 1,5\n2,1 2,2 2,3 2,4 2,5\n3,1 3,2 3,3 3,4 3,5\n4,1 4,2 4,3 4,4 4,5\n5,1 5,2 5,3 5,4 5,5\nwhat is the probability that the first number selected was 3 or higher, given that the sum of the two numbers was 7?\na. $\frac{3}{25}$\nb. $\frac{4}{25}$\nc. $\frac{1}{5}$\nd. $\frac{3}{4}$

a computer is programmed to select two random numbers from 1 to 5. all possible outcomes are shown in the table. each outcome has equal probability.\n1,1 1,2 1,3 1,4 1,5\n2,1 2,2 2,3 2,4 2,5\n3,1 3,2 3,3 3,4 3,5\n4,1 4,2 4,3 4,4 4,5\n5,1 5,2 5,3 5,4 5,5\nwhat is the probability that the first number selected was 3 or higher, given that the sum of the two numbers was 7?\na. $\frac{3}{25}$\nb. $\frac{4}{25}$\nc. $\frac{1}{5}$\nd. $\frac{3}{4}$

Answer

Answer:

C. $\frac{1}{5}$

Explanation:

Step1: List pairs with sum 7

$(2,5),(3,4),(4,3),(5,2)$

Step2: Count pairs with first - number ≥ 3

There are 2 pairs: $(3,4),(4,3),(5,2)$ where the first number is 3 or higher out of 4 pairs with sum 7.

Step3: Calculate probability

The probability is $\frac{2}{10}=\frac{1}{5}$ since there are 10 total pairs with sum 7 (from the sample space) and 2 of them meet the condition.