Question

Two coins are tossed simultaneously. The probability of getting atmost one head is :

• A. \(\frac{1}{4}\)
• B. \(\frac{3}{4}\)
• C. \(\frac{1}{2}\)
• D. \(\frac{5}{4}\)

Hint:

When tossing two coins, the possible outcomes are: HH, HT, TH, TT (4 total outcomes). "Atmost one head" means:
0 Heads: TT (1 outcome)
1 Head: HT, TH (2 outcomes) Total favorable outcomes = 1 + 2 = 3. Probability = Favorable / Total = \(3/4\). Alternatively, "atmost one head" is the opposite of "atleast two heads" (which means exactly two heads in this case: HH). P(HH) = 1/4. P(atmost one head) = 1 - P(HH) = \(1 - 1/4 = 3/4\).

Answer 1

The Correct Option is B

Concept: Probability is calculated as the ratio of the number of favorable outcomes to the total number of possible outcomes. Probability (\(P\)) = \(\frac{\text{Number of Favorable Outcomes}}{\text{Total Number of Possible Outcomes}}\) Step 1: List all possible outcomes (Sample Space) When two coins are tossed simultaneously, let H denote a Head and T denote a Tail. The possible outcomes are:
HH (Both heads)
HT (First coin head, second coin tail)
TH (First coin tail, second coin head)
TT (Both tails) The total number of possible outcomes is 4. Step 2: Identify the favorable outcomes for "atmost one head" "Atmost one head" means zero heads OR one head. Let's list the outcomes that satisfy this condition:
Zero heads: TT (This outcome has 0 heads, which is atmost 1 head)
One head:
HT (This outcome has 1 head)
TH (This outcome has 1 head) The favorable outcomes are TT, HT, TH. The number of favorable outcomes is 3. Alternative way to think about "atmost one head": It means we do NOT want the outcome with two heads (HH). So, favorable outcomes = Total outcomes - Outcome with two heads Favorable outcomes = \{HH, HT, TH, TT\} - \{HH\} = \{HT, TH, TT\}. Number of favorable outcomes = 3. Step 3: Calculate the probability Probability (atmost one head) = \(\frac{\text{Number of favorable outcomes}}{\text{Total number of possible outcomes}}\) \[ P(\text{atmost one head}) = \frac{3}{4} \] Step 4: Compare with the options The calculated probability is \(\frac{3}{4}\). This matches option (2).