Harpreet tosses two different coins simultaneously (say, one is of \rupee1 and other of \rupee2). What is the probability that she gets at least one head?
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Step-by-Step Solution
Step 1: Define outcomes for each coin
When a coin is tossed, there are two possible outcomes: Head (H) or Tail (T). We consider the outcomes for each of the two different coins Harpreet tosses.
Step 2: List all possible outcomes
Since two coins are tossed simultaneously, we list all possible paired outcomes. The first element in each pair represents the outcome of the \rupee1 coin and the second represents the outcome of the \rupee2 coin. The total number of possible outcomes is 4.
Step 3: Identify favorable outcomes
The problem asks for the probability of getting at least one head. This means we are interested in outcomes where there is one head or two heads. We identify these specific outcomes from our sample space.
Step 4: Count number of favorable outcomes
From the favorable outcomes identified in the previous step, we count how many distinct outcomes satisfy the condition of having at least one head.
Step 5: Count total number of outcomes
From the sample space, we count the total number of possible outcomes when two coins are tossed simultaneously.
Step 6: Calculate the probability
The probability of an event is calculated by dividing the number of outcomes favorable to the event by the total number of possible outcomes in the sample space. Substituting the values we found, we get the probability.
Step 7: Substitute values and find the final probability
By substituting the number of favorable outcomes, n(E)=3, and the total number of outcomes, n(S)=4, into the probability formula, we obtain the final probability.