Question

Mandy has a bag contain one red, one yellow and one blue block, and a fair coin. She chooses one block from the bag and then tosses the coin. She conducted 20 trials. Here are her results below:

What is the experimental probability of drawing a blue block and flipping heads?

What is the theoretical probability of drawing a blue block and flipping heads. Draw a tree diagram to represent this situation and find the theoretical probability

What is the experimental probability of drawing the yellow block and flipping tails? *
What is the theoretical probability of drawing the yellow block and flipping tails?

Answer 1

P_exp(blue and heads) = 20%

P_the(blue and heads) = 16.67%

P_exp(yellow and tails) = 15%

P_the(yellow and tails) = 16.67%

Explanation:

To find the experimental probability of drawing a blue block and flipping heads, we need to check in the table the cases where this occurs.

The cases are: 5, 6, 10 and 17

So there are 4 cases in a total of 20 cases, then the probability is 4/20 = 0.2 = 20%

The theoretical probability is the probability of having a blue block among the 3 blocks, and having a heads in the coin. The first one is 1/3 and the second is 1/2, so the probability is (1/3)*(1/2) = 1/6 = 0.1667 = 16.67%

The experimental probability of drawing the yellow block and flipping tails occurs at 3, 7, and 9 (3 cases), so the probability is 3/20 = 0.15 = 15%

The theoretical probability of drawing the yellow block and flipping tails is (1/3) * (1/2) = 1/6 = 0.1667 = 16.67%