Question

help

Answer 1

If the probability of making a penalty shot is 77.6%, then the probability of missing a penalty shot is 1 - 0.776 = 0.224.

The probability of missing at least one shot in two attempts is equal to the probability of missing the first shot and making the second shot, or making the first shot and missing the second shot, or missing both shots.

So, the probability of missing at least one shot in two attempts is:

P(miss at least one shot) = P(miss first shot and make second shot) + P(make first shot and miss second shot) + P(miss both shots)
P(miss at least one shot) = (0.224 x 0.776) + (0.776 x 0.224) + (0.224 x 0.224)
P(miss at least one shot) = 0.345856

Therefore, the probability of missing at least one shot in two attempts is approximately 0.3459 or 34.59%.

If the soccer player taking two penalty shots is simulated 2500 times, then we would expect about 0.3459 x 2500 = 864 simulations to result in at least one missed shot.