Question

A box contains four tiles, numbered 1,4,5, and 8. Kelly randomly chooses one tile, places it back in the box, then chooses a second tile. What is the probability that the sum of the two chosen tiles is greater than 7?

Answer 1

Given:

A box contains four tiles, numbered 1,4,5, and 8. Kelly randomly chooses one tile, places it back in the box, then chooses a second tile.

To find:

The probability that the sum of the two chosen tiles is greater than 7.

Solution:

A box contains four tiles, numbered 1,4,5, and 8. So, the total possible outcomes are:

S = {(1,1),(1,4),(1,5),(1,8),(4,1),(4,4),(4,5),(4,8),(5,1),(5,4),(5,5),(5,8),(8,1),(8,4),(8,5),(8,8)}

n(S) = 16

A : Sum of the two chosen tiles is greater than 7.

A = {(1,8),(4,4),(4,5),(4,8),(5,4),(5,5),(5,8),(8,1),(8,4),(8,5),(8,8)}

n(A) = 11

So, probability that the sum of the two chosen tiles is greater than 7 is

$Probability=\dfrac{n(A)}{n(S)}$

$Probability=\dfrac{11}{16}$

Therefore, the required probability is $\dfrac{11}{16}$.