84. The probability of successfully performing an exercise for each of two athletes is 0.5. The athletes perform the exercise in turns, with each making two attempts. The one who performs the exercise first wins the prize. Find the probability of the athletes winning the prize.
Solution. For the prize to be awarded, it is sufficient for at least one of the four attempts to be successful. The probability of a successful attempt is $p=0.5$, and of an unsuccessful attempt is $q=1-0.5=0.5$. The desired probability is

$$
P=1-q^{4}=1-0.5^{4}=0.9375
$$