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Probability

- Event: Any subset of a sample space is called an event.
- Probability of Occurrence of an Event: Let S be the sample space and let E be an event.

Then, E⊆S

∴ P(E) =

- Sample space: When we perform an experiment, then the set S of all possible outcomes is called the Sample space.

Ques1. In a simultaneous throw of two coins, the probability of getting at least one head is:

- ) c.) d.) e.) None of these

Explanation: Answer is D

Here S = {HH, HT, TH, TT}

Let E = event of getting at least one head = {HT, TH, HH}

∴ P(E) = =

Ques2. Three unbiased coins are tossed. What is the probability of getting at least 2 heads?

- ) c.) d.) e.) None of these

Explanation: Answer is B

Here S = {TTT, TTH, THT, HTT, THH, HTH, HHT, HHH}

Let E = event of getting at least two heads = {THH, HTH, HHT, HHH}

∴ P(E) = = =

Ques3. Three unbiased coins are tossed. What is the probability of getting at most 2 heads?

- ) c.) d.) e.) None of these

Explanation: Answer is D

Here S = {TTT, TTH, THT, HTT, THH, HTH, HHT, HHH}

Let E = event of getting at most two heads

Then, E = {TTT, TTH, THT, HTT, THH, HTH, HHT}

∴ P(E) = =

Ques4. In a single throw of a dice, what is the probability of getting a number greater than 4?

- ) c.) d.) e.) None of these

Explanation: Answer is B

When a dice is thrown, we have S = {1, 2, 3, 4, 5, 6}

Let E = event of getting a number greater than 4 = {5, 6}

∴ P(E) = = =

Ques5. In a simultaneous throw of two dice, what is the probability of getting a total of 7?

- ) c.) d.) e.) None of these

Explanation: Answer is A

We know that in a simultaneous throw of two dice, n(S) = 6 * 6 = 36

Let E = event of getting a total of 7 = {(1,6), (2,5), (3,4), (4,3), (5,2), (6,1)}

∴ P(E) = = =