Home
Class 12
MATHS
A coin is tossed three times, consider t...

A coin is tossed three times, consider the following events. A : No head appears, B: Exactly one head appears and C: Atleast two appear. Do they form a set of mutually exclusive and exhaustive events?

Text Solution

Verified by Experts

The sample space of the experiment is
`S = {HHH,HHT,HTH,THH,HT T,THT,T TH,T T T}`
`A = {T T T}`
`B = {HT T, THT, T TH}`
`C = {HHT, HTH, THH, HHH}`
Now, `A uu B uu C = {T T T, HT T, THT, T TH, HHT, HTH, THH, HHH} = S`
Therefore, A, B and C are exhaustive events.
Also, `A nn B = phi, A nn C = phi and B nn C = phi`
Therefore, A, B and C form a set of mutually exclusive and exhaustive events.
Promotional Banner

Topper's Solved these Questions

  • PROBABILITY I

    CENGAGE ENGLISH|Exercise Solved Example|9 Videos

  • PROBABILITY I

    CENGAGE ENGLISH|Exercise Exercise 9.1|6 Videos

  • PROBABILITY

    CENGAGE ENGLISH|Exercise Comprehension|2 Videos

  • PROBABILITY II

    CENGAGE ENGLISH|Exercise MULTIPLE CORRECT ANSWER TYPE|6 Videos

Similar Questions

Explore conceptually related problems

A coin and a die are tossed . Describe the following events . D : getting a head or a tail.

A coin is tossed two times. Find the probability of getting atmost one head.

A coin and a die are tossed . Describe the following events . A : getting a head even number ,

A coin is tossed three times. Given that at least one head appears, what is the probability that exactly two heads will appear?

A coin is tossed 15 times, then find the probability that exactly 9 consecutive heads appears, is

When a coin is tossed write two events which are mutually exclusive and exhausitve.

A coin is tossed 4 times . The probability of getting atleast one head is

If a coin is tossed n times, then find the probability that the head appears odd number of times.

A coin is tossed three times. Event A: two heads appear Event B: last should be head Then identify whether events A and B are independent or not.

A fair coin is tossed three times. Consider the events A = {First toss is head} B = {Second toss is head} C = {Exactly two heads in a raw} Which of the following statements is true?