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Two coins are tossed simultaneously. What is the probability of getting at least one head?
1/4
1/2
3/4
1
3/4
Instead of calculating for 1 head and 2 heads, simply calculate the probability of the complementary event (zero heads) and subtract it from 1. Total outcomes = 4, outcomes with no head = 1 (TT), so 1тИТ1/4=3/4.
Two fair coins are tossed simultaneously, leading to a sample space of all possible head and tail combinations.
P(A)=1тИТP(Ac)
Instead of calculating for 1 head and 2 heads, simply calculate the probability of the complementary event (zero heads) and subtract it from 1. Total outcomes = 4, outcomes with no head = 1 (TT), so 1тИТ1/4=3/4.
Many students mistake 'at least one' for 'exactly one' and calculate only the cases {HT, TH}, forgetting to include the {HH} case.
Define Sample Space
When two coins are tossed, each coin has 2 outcomes (Head or Tail). Total possible outcomes are 2├Ч2=4, which are S={HH,HT,TH,TT}.
n(S)=4
Identify Complementary Event
The event A is 'at least one head'. The complement Ac is 'no heads', which corresponds to the outcome TT.
P(Ac)=41тАЛ
Calculate Required Probability
Using the law of complement events, we subtract the probability of the unwanted case from the total probability space.
P(A)=1тИТ41тАЛ=43тАЛ
C is correct because the probability of getting no heads is 1/4, and subtracting this from 1 gives 3/4.
This '1 minus complement' strategy is a vital time-saver in competitive exams for 'at least' probability questions involving multiple dice or coins.