Question

In a single toss of a fair die, the odds against the event that number 4 or 5 turns up is

• A. \(2 : 1\)
• B. \(1 : 3\)
• C. \(2 : 3\)
• D. \(1 : 1\)

Hint:

Do not confuse probability with odds. Odds against = unfavourable : favourable.

Answer 1

The Correct Option is A

Step 1: Understanding the Concept:
"Odds against" an event \(E\) is the ratio of unfavorable outcomes to favorable outcomes.
Step 2: Key Formula or Approach:
Odds against \(E = \frac{P(E')}{P(E)} = \frac{\text{Unfavorable outcomes}}{\text{Favorable outcomes}}\).
Step 3: Detailed Explanation:
In a single toss of a die, the sample space is \(S = \{1, 2, 3, 4, 5, 6\}\). Total outcomes = 6.
The event is \(E = \{4, 5\}\).
Number of favorable outcomes \(n(E) = 2\).
Number of unfavorable outcomes \(n(E') = 6 - 2 = 4\).
The unfavorable outcomes are \(\{1, 2, 3, 6\}\).
Odds against \(E = n(E') : n(E) = 4 : 2\).
Simplifying the ratio: \(2 : 1\).
Step 4: Final Answer:
The odds against are \(2 : 1\).