Question

Daniel has 1 blue pencil and 5 yellow pencils in his backpack. He also has 2 pink erasers, 4 tan erasers, and 3 gray erasers in his backpack. If Daniel randomly selects one pencil and one eraser from his backpack, what is the probability that he will select a blue pencil and a gray eraser?

Answer 1

the correct answer is 4/15

Answer 2

Answer: $\dfrac{1}{18}$

Step-by-step explanation:

Given : Daniel has 1 blue pencil and 5 yellow pencils in his backpack.

Then, the probability of selecting a blue pencil :-

$\dfrac{\text{Number of blue pencil}}{\text{Total pencil}}\\\\=\dfrac{1}{1+5}=\dfrac{1}{6}$

He also has 2 pink erasers, 4 tan erasers, and 3 gray erasers in his backpack.

Then, the probability of selecting a gray eraser :-

$\dfrac{\text{Number of gray erasers}}{\text{Total erasers}}\\\\=\dfrac{3}{2+4+3}=\dfrac{3}{9}\\\\=\dfrac{1}{3}$

Since both the event are independent of each other.

Then, the probability that he will select a blue pencil and a gray eraser will be :-

$\dfrac{1}{6}\times\dfrac{1}{3}=\dfrac{1}{18}$

Hence, the probability that he will select a blue pencil and a gray eraser $=\dfrac{1}{18}$