A coin is tossed four times. Assuming the coin is equally likely to land on heads or tails, compute the probability of the event occurring. (Enter your probability as a fraction.)
2 heads and 2 tails
To calculate the probability of getting 2 heads and 2 tails when a coin is tossed four times, we need to consider the total number of possible outcomes and the number of favorable outcomes.
Total number of outcomes when a coin is tossed four times = 2^4 = 16 (each toss has 2 possibilities: heads or tails)
Number of favorable outcomes (2 heads and 2 tails) = number of ways to choose 2 positions out of 4 for heads * number of ways to choose 2 positions out of the remaining 2 for tails = (4 choose 2) * (2 choose 2) = 6 * 1 = 6
Therefore, the probability of getting 2 heads and 2 tails when a coin is tossed four times is:
Number of favorable outcomes / Total number of outcomes = 6 / 16 = 3 / 8
So the probability is 3/8.