Question

Anna is learning how to do a back flip. She is successful 50% of the time. As her gymnastics competition approaches, Anna practices every day. The day before competition she would like to determine the probability of completing her back flip successfully 8 out of 10 times. Design a simulation that Anna could use in this situation.

Answer 1

P(8; 10, 0.50) = 4.39%

There is 4.39% probability that Anna will complete her back flip successfully 8 out of 10 times.

Explanation:

The given problem can be modeled as a binomial experiment since the following conditions are satisfied.

• There are n repeated trials and are independent of each other.

• There are only two possibilities: Anna is successful in doing a back flip or Anna is unsuccessful in doing a back flip.

• The probability of success does not change with trial to trial.

The binomial distribution is given by

P(x; n, p) = nCx pˣ (1 - p)ⁿ⁻ˣ

Where p is the probability that Anna is successful in doing a back flip and 1 - p is the probability that Anna is unsuccessful in doing a back flip, n is number of trials and x is the variable of interest.

In this case, we have x = 8, n = 10 and p = 0.50

P(8; 10, 0.50) = (10C8)*(0.50)⁸*(1 - 0.50)¹⁰⁻⁸

P(8; 10, 0.50) = (45)*(0.50)⁸*(0.50)²

P(8; 10, 0.50) = 0.0439

P(8; 10, 0.50) = 4.39%

Therefore, there is 4.39% probability that Anna will complete her back flip successfully 8 out of 10 times.