Correct Answer - Option 5 : 0.5
Two coins are flipped one after another.
Formula and Concept Used:
The probability of occurrence of an event E, within a sample space S, is given by:
P(E) = n(E) / n(S)
where P(E) = probability of occurrence of the event E,
n(E) = number of times the event E occurs, and
n(S) = number of points in the sample space S.
In the case of two independent events, the probability of the first event does not affect the probability of the second event.
When a coin is tossed, we obtain either head or tail.
∴ n(S) = 2
Number of times head occurs, when a coin is tossed = 1
∴ n(E) = 1
∴ The probability of obtaining a head, when a coin is tossed = 1/2 = 0.5
Similarly, the probability of obtaining a tail = 0.5
But, the tossing of the two coins are independent events, because the outcome of the first experiment doesn't affect the outcome of the second.
∴ The probability that tail comes up on the second coin, if a head appears on the first coin is 0.5
It is important to note here that if the student forgets the concept of independent events, then the answer would be obtained as
0.5 × 0.5 = 0.25,
which is wrong.
Hence, it is important to note that both these events are independent of each other.