Question

1. answer each probability question.

a) design a bag of marbles where the theoretical probability of picking blue is $\frac{2}{5}$.
b) if you flip a coin ten times and get tails three times:
what is the experimental probability of getting heads?
what is the experimental probability of getting tails?
what is the theoretical probability of getting heads?

Explanation:

Step1: Recall probability formula

Experimental probability = $\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}$. Theoretical probability of a fair - coin flip for heads or tails is $\frac{1}{2}$.

Step2: Solve part (a)

To have a theoretical probability of picking blue as $\frac{2}{5}$, we can have a bag with 5 marbles in total and 2 blue marbles. For example, 2 blue, 1 green, 2 brown (the non - blue colors can be any combination as long as the total number of non - blue marbles is 3).

Step3: Solve part (b) for experimental probability of heads

The coin is flipped 10 times and tails is gotten 3 times. So the number of heads is $10 - 3=7$. The experimental probability of getting heads is $\frac{7}{10}$ since the number of favorable outcomes (heads) is 7 and the total number of outcomes is 10.

Step4: Solve part (b) for experimental probability of tails

The number of tails is 3 and the total number of flips is 10. So the experimental probability of getting tails is $\frac{3}{10}$.

Step5: Solve part (b) for theoretical probability of heads

For a fair coin, the theoretical probability of getting heads is $\frac{1}{2}$ because there are 2 equally likely outcomes (heads or tails) and 1 of them is heads.

Answer:

a) A bag with 2 blue, 1 green and 2 brown marbles (answers may vary as long as there are 2 blue marbles out of 5 total marbles).
b) Experimental probability of getting heads: $\frac{7}{10}$
Experimental probability of getting tails: $\frac{3}{10}$
Theoretical probability of getting heads: $\frac{1}{2}$