Suppose you will be attending 6 hockey games. If each game independently will go to overtime with probability
0.10, find the probabililty that:
a) at least one of the games will go into overtime
To find the probability that at least one game will go into overtime, we need to find the probability that none of the games go into overtime and subtract it from 1.
The probability that a game does not go into overtime is 1 minus the probability that it goes into overtime. In this case, the probability that a game does not go into overtime is 1 - 0.10 = 0.90.
Since each game's outcome is independent, we can calculate the probability that none of the games go into overtime by multiplying the probabilities of each game not going into overtime.
Number of games = 6
Probability that none of the games go into overtime = (0.90)^6
Now, to find the probability that at least one game will go into overtime, we subtract the probability that none of the games go into overtime from 1.
Probability of at least one game going into overtime = 1 - (0.90)^6
Calculating this expression gives us the desired probability.
To find the probability that at least one of the games will go into overtime, we can use the concept of complement rule.
The complement of "at least one of the games will go into overtime" is "none of the games will go into overtime". So, we need to find the probability of none of the games going into overtime and subtract it from 1.
The probability of each game not going into overtime is 1 - 0.10 = 0.90.
Therefore, the probability that none of the 6 games will go into overtime is (0.90)^6 = 0.53144.
Finally, the probability that at least one of the games will go into overtime is 1 - 0.53144 = 0.46856, or 46.86%.