If four coins are flipped at once, find the probability that there will be at least 2 heads. Round your answer to 3 decimal places.
To find the probability of a specific event, we need to divide the number of favorable outcomes by the total number of possible outcomes.
Let's consider the possible outcomes when flipping four coins. Each coin has two possible outcomes: heads or tails. So, for four coins, we have a total of 2^4 = 16 possible outcomes.
Now, let's determine the number of favorable outcomes (at least 2 heads). We can do this by considering the complementary event, which is having fewer than 2 heads (0 or 1 head).
Number of outcomes with 0 heads: There is only one outcome with 0 heads, which is all four coins landing on tails (TTTT).
Number of outcomes with 1 head: To determine this, we need to consider the various combinations. There are 4 ways to choose which coin will be heads, and for each choice, the remaining 3 coins will be tails. So, there are a total of 4 possible outcomes with 1 head (HTTT, THTT, TTHT, TTTH).
So, the number of favorable outcomes (fewer than 2 heads) is 1 (0 heads) + 4 (1 head) = 5.
Now, the probability of getting at least 2 heads can be determined as follows:
P(at least 2 heads) = 1 - P(fewer than 2 heads)
P(at least 2 heads) = 1 - (number of favorable outcomes / total number of outcomes)
P(at least 2 heads) = 1 - (5 / 16)
P(at least 2 heads) = 1 - 0.3125
P(at least 2 heads) = 0.6875 (rounded to 3 decimal places)
Therefore, the probability is 0.688.