Q37.Marks: +2.0UGC NET Paper 2: Computer Sc 23rd August 2024 Shift 1
A coin is tossed successively three times. Find the Probability (P), Event (E), Sample space (S) of getting exactly one head or two heads, where n is number of occurrence.
(A) n(S) = 8 and n(E) = 4
(B) n(E) = 6 and n(S) = 8
(C) P(E) = \(\frac{3}{4}\)
(D) P(E) = \(\frac{1}{2}\)
Choose the correct answer from the options given below:
1.(A), (B), (C) and (D)
2.(B) and (C) Only ✓ Correct
3.(A) and (D) Only
4.(C) and (D) Only
Solution
The correct answer is 2)(B) and (C) Only
EXPLANATION:
Let's first understand the problem:
A coin is tossed successively three times. We need to find the Probability (P), Event (E), and Sample space (S) of getting exactly one head or two heads, where n is the number of occurrences.
Sample Space (S): The sample space for tossing a coin three times is given by the set of all possible outcomes:
S = {HHH, HHT, HTH, HTT, THH, THT, TTH, TTT}
So, n(S) = 8
Event (E): The event of getting exactly one head or two heads includes the following outcomes:
E = {HTT, THT, TTH, HHT, HTH, THH}
So, n(E) = 6
Probability (P): The probability of an event is given by the ratio of the number of favorable outcomes to the total number of possible outcomes:
P(E) = n(E) / n(S) = 6 / 8 = 3/4
Now, let's evaluate the options:
(A) n(S) = 8 and n(E) = 4 -
This statement is NOT CORRECT. While n(S) = 8 is correct, n(E) = 4 is incorrect as n(E) = 6.
(B) n(E) = 6 and n(S) = 8 -
This statement is CORRECT. As calculated, n(E) = 6 and n(S) = 8.
(C) P(E) = 3/4 -
This statement is CORRECT. As calculated, P(E) = 3/4.
(D) P(E) = 1/2 -
This statement is NOT CORRECT. The correct probability is P(E) = 3/4, not 1/2.