Probability of getting exactly two heads

To find the probability of getting exactly two heads when three coins are rolled, we need to consider all the possible outcomes and determine the number of favorable outcomes.

Step 1: Define the sample space

The sample space consists of all the possible outcomes when rolling three coins. Each coin can either land on heads (H) or tails (T), so there are 2^3 = 8 possible outcomes:

HHH, HHT, HTH, HTT, THH, THT, TTH, TTT

Step 2: Determine the favorable outcomes

To find the number of favorable outcomes, we need to identify the outcomes where there are exactly two heads. From the sample space, we can see that there are three outcomes that satisfy this condition: HHT, HTH, and THH.

Step 3: Calculate the probability

The probability of an event is given by the number of favorable outcomes divided by the number of possible outcomes. In this case, we have three favorable outcomes and eight possible outcomes, so the probability of getting exactly two heads is:

P(exactly two heads) = favorable outcomes / possible outcomes
P(exactly two heads) = 3/8

Therefore, the probability of getting exactly two heads when three coins are rolled is 3/8 or 0.375.

Summary:

- The probability of getting exactly two heads when three coins are rolled is 3/8 or 0.375.
- The sample space consists of 8 possible outcomes: HHH, HHT, HTH, HTT, THH, THT, TTH, TTT.
- There are three favorable outcomes: HHT, HTH, and THH.
- The probability is calculated by dividing the number of favorable outcomes by the number of possible outcomes.
- The formula used is P(exactly two heads) = 3/8.