Question

A coin is tossed A times and it showed tail B times. The probability of getting one head is :

• A. \(\frac{b}{a}\)
• B. \(\frac{b}{a+b}\)
• C. \(\frac{a-b}{a}\)
• D. \(\frac{b-a}{a}\)

Hint:

1. Total number of times the coin is tossed = \(a\). 2. Number of times tails appeared = \(b\). 3. Therefore, the number of times heads appeared = Total tosses - Tails = \(a - b\). 4. The probability of an event is (Number of times the event occurred) / (Total number of trials). 5. Probability of getting a head = (Number of heads) / (Total tosses) = \(\frac{a-b}{a}\).

Answer 1

The Correct Option is C

Concept: Probability of an event is defined as the ratio of the number of favorable outcomes to the total number of possible outcomes. In this case, we are dealing with experimental probability based on observed frequencies. Step 1: Identify the given information Let 'a' be the total number of times the coin is tossed. Let 'b' be the number of times a tail showed up. (The question uses capital A and B, but options use lowercase a and b. We will use lowercase a and b consistent with the options).
Total number of trials (tosses) = \(a\)
Number of times tail appeared = \(b\) Step 2: Determine the number of times head appeared A coin toss has two possible outcomes: head or tail. If the coin was tossed 'a' times and 'b' of those were tails, then the remaining tosses must have resulted in heads. Number of times head appeared = Total tosses - Number of tails Number of heads = \(a - b\) Step 3: Calculate the probability of getting one head The question asks for "The probability of getting one head". This is interpreted as the experimental probability of a single toss resulting in a head, based on the observed data. Probability of an event = \(\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}\) In this context:
Favorable outcome = getting a head
Number of favorable outcomes observed = Number of heads = \(a - b\)
Total number of trials (outcomes observed) = \(a\) So, the probability of getting a head, P(Head), is: \[ P(\text{Head}) = \frac{\text{Number of heads}}{\text{Total number of tosses}} = \frac{a-b}{a} \] Step 4: Compare with the given options The calculated probability is \(\frac{a-b}{a}\). This matches option (3).