Question

Isaiah scores with 50% of his penalty kicks in soccer. He flips two fair coins to conduct a simulation with 20 trials to determine the likelihood that he will make his next two penalty kicks, as shown. Heads up (H) represents a goal. What is the probability that Isaiah will make both penalty kicks? Give the probability as a percent. Enter your answer in the box.

Answer 1

Answer:

The probability that Isaiah will make both penalty kicks is 25%.

Step-by-step explanation:

We are given that Isaiah scores with 50% of his penalty kicks in soccer.

He flips two fair coins to conduct a simulation with 20 trials to determine the likelihood that he will make his next two penalty kicks.

The above situation can be represented through binomial distribution;

$P(X =r) = \binom{n}{r} \times p^{r} \times (1-p)^{n-r};x=0,1,2,3,......$

where, n = number of trials (samples) taken = 2 penalty kicks

           r = number of success = make both penalty kicks

           p = probability of success which in our question is probability  

                 that Isaiah scores with his penalty kicks, i.e; p = 50%

Let X = Number of penalty kicks made by Isaiah

So, X ~ Binom(n = 2 , p = 0.50)

Now, Probability that Isaiah will make both penalty kicks is given by = P(X = 2)

                     P(X = 2) =  $\binom{2}{2} \times 0.50^{2} \times (1-0.50)^{2-2}$

                                   =  $1 \times 0.50^{2} \times 0.50^{0}$

                                   =  0.25 or 25%

Hence, the probability that Isaiah will make both penalty kicks is 25%.