Exercise · ZW-CLASSICAL-PROBABILITY-007 · ★★☆ Intermediate
Two fair dice are rolled. What is the probability of getting at least one 6?
Choose one option.
Show answer
- A. \(\frac{11}{36}\)
Explanation
It is easier to count the complement: no 6 occurs in \(5\cdot5=25\) pairs, so the probability is \(1-\frac{25}{36}=\frac{11}{36}\). Adding \(\frac16+\frac16=\frac13\) counts the pair \((6,6)\) twice.
Review the concept: Classical probability
The classical probability \(P(A)\) of an event \(A\), when the sample space \(\Omega\) is finite with equally likely outcomes, is the ratio of favorable to possible outcomes.
\[P(A)=\frac{|A|}{|\Omega|}\]
More practice problems: classical probability
- ZW-CLASSICAL-PROBABILITY-001 A fair die is rolled. What is the probability of getting a number greater than 4?
- ZW-CLASSICAL-PROBABILITY-002 A fair coin is tossed three times. What is the probability of getting exactly two heads?
- ZW-CLASSICAL-PROBABILITY-003 Two fair dice are rolled. What is the probability that the sum is 7?
- ZW-CLASSICAL-PROBABILITY-004 One card is drawn at random from a standard 52-card deck. What is the probability that it is a hear…
- ZW-CLASSICAL-PROBABILITY-005 An urn has 5 red balls and 3 blue balls. One ball is drawn at random. What is the probability that…
- ZW-CLASSICAL-PROBABILITY-006 Two fair dice are rolled. What is the probability that the sum is at least 9?
- ZW-CLASSICAL-PROBABILITY-008 Two cards are drawn at random, without replacement, from a 52-card deck. What is the probability th…
- ZW-CLASSICAL-PROBABILITY-009 Two fair coins are tossed and someone reasons with Omega=\0,1,2\ heads: “P(one head)=13”. What is t…
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