Question

Two different coins are tossed simultaneously. What is the probability of getting :
(i) at least one head ?
(ii) at most one tail ?
(iii) a head and a tail ?

Hint:

"At least one head" and "At most one tail" in a two-coin toss describe the exact same set of outcomes. Writing down the sample space clearly is the safest way to avoid confusion with words like "at least" and "at most".

Answer 1

Step 1: Understanding the Concept:
When two coins are tossed, the sample space \(S\) consists of all possible outcomes.
\(S = \{HH, HT, TH, TT\}\)
Total number of outcomes \(n(S) = 4\).
Step 3: Detailed Explanation:
(i) At least one head:
Favorable outcomes: \(\{HH, HT, TH\}\).
Number of favorable outcomes = 3.
Probability = \(3/4\).
(ii) At most one tail:
"At most one" means 0 tails or 1 tail.
Favorable outcomes: \(\{HH, HT, TH\}\).
Number of favorable outcomes = 3.
Probability = \(3/4\).
(iii) A head and a tail:
Favorable outcomes: \(\{HT, TH\}\).
Number of favorable outcomes = 2.
Probability = \(2/4 = 1/2\).
Step 4: Final Answer:
(i) \(3/4\), (ii) \(3/4\), (iii) \(1/2\).