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

The answer is 35%

Explanation:

Trust me ive taken this test before.

Answer 2

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

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} * p^(r) * (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} * 0.50^(2) * (1-0.50)^(2-2)`

=
`1 * 0.50^(2) * 0.50^(0)`

= 0.25 or 25%

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