Question

If a coin is tossed twice, what are the chances that one toss will land heads – up and the other will land tails – up?
(A). One in three
(B). One in two
(C). Two in five
(D). Two to one

Answer 1

Hint: First write all possibilities when a coin is thrown twice. Now count the number of possibilities which are as required. Now use the probability formula to get the result you require.
$\text{Probability} = \dfrac{\text{Favorable possibilities}}{\text{Total possibilities}}$.

Complete step-by-step solution -
Probability: In a simple way, the probability is how likely something is to happen. Whenever we’re unsure about the outcome of an event we talk about probabilities. It is the value which lies between 0 and 1. Probability is the division result of favorable outcomes, total outcomes.
Probability = Favorable possibilities / Total possibilities.
Given the condition of the event in the question is written as:
A coin is tossed twice and takes note of outcome in each toss. Here we have 2 coins with 2 possibilities head, tail. We assume that the coin we toss is an unbiased one.
So, the outcomes of the event can be written as:
(Head, tail); (tail, Head); (tail, tail); (Head, Head)
In the bracket, the first term represents the first outcome of the toss.
In the bracket, the second term represents the second outcome of the toss.
Here we need the possibility of 1 head, 1 tail in 2 tosses.
So, favorable outcomes = 2, whereas total = 4.
By using the formula of probability, we get that:
Chances = \[\dfrac{2}{4}=\dfrac{1}{2}\]
So, the probability that we have one heads-up and one tail up in the two tosses is given by \[\dfrac{1}{2}\].
Therefore option (b) is correct.

Note: Don’t forget that 2 tosses are different. So, we must consider (Tail, Head) & (Head, Tail) as different possibilities. So, the total will be 4. Generally, students take it as 3. Always remember whenever you see the word chances of happening in a question use the concept of probability. Also make a note that the outcome, possibility are the same words.