Probability of At Least 2 Heads When 4 Coins are Thrown

To determine the probability of getting at least 2 heads when 4 coins are thrown, we need to consider all possible outcomes and calculate the probability of each outcome.

Step 1: Identify the Sample Space

The sample space refers to all possible outcomes of an experiment. In this case, when 4 coins are thrown, the sample space can be represented as:

S = {HHHH, HHHT, HHTH, HHTT, HTHH, HTHT, HTTH, HTTT, THHH, THHT, THTH, THTT, TTHH, TTHT, TTTH, TTTT}

Step 2: Identify the Desired Outcomes

To determine the probability of getting at least 2 heads, we need to identify the outcomes that meet this criteria. In this case, the desired outcomes are those with 2, 3, or 4 heads. Let's list them:

HHTT, HTHT, HTTH, TTHH, THHT, THTH, HTHH, HHHT, HHTH, THHH

Step 3: Calculate the Probability of Each Desired Outcome

To calculate the probability of each desired outcome, we need to determine the number of ways each outcome can occur and divide it by the total number of possible outcomes.

- There are 6 outcomes with 2 heads: HHTT, HTHT, HTTH, TTHH, THHT, THTH.
- There are 4 outcomes with 3 heads: HTHH, HHHT, HHTH, THHH.
- There is 1 outcome with 4 heads: HHHH.

Step 4: Calculate the Total Probability

To calculate the total probability, we sum up the probabilities of all the desired outcomes.

Probability = (Number of desired outcomes) / (Total number of possible outcomes)
Probability = (6 + 4 + 1) / 16
Probability = 11 / 16
Probability = 0.6875 or 68.75%

Therefore, the probability of getting at least 2 heads when 4 coins are thrown is 0.6875 or 68.75%.

Given question probability = 11/16