Which of the following is not a sample space for the...

Which of the following is not a sample space for the experiment of flipping a coin 3 times? A. {all flips are the same, there is exactly one tail, there are exactly two tails} B. {there is exactly one head, all flips are the same} C. {all the flips are heads, exactly two tails are flipped, there are an odd number of tails} D. {all the flips are heads, there are an odd number of tails, exactly one head is flipped} E. {all flips are the same, there is at least one head and at least one tail}

Transcript

00:01 Hello students in this question we have been given that the three coins are flipped three coins are flipped so we have to determine which of these are not the sample sample space of these events so sample space of three coins are flipped is equal to going to be two multiplied by two multiplied by two which is equal to eight so these are the conditions which i'm going to be writing so let me write that.

00:31 So first option is all fields are same.

00:33 There is exactly one tail and there is exactly two tails.

00:36 So for all fields are same is going to be means all our heads and all are tails.

00:45 So this is all fields are same.

00:47 And there is exactly one tail means whether it is head head tail or head tail or tail head tail or tail head head.

00:56 Head and there is a active two tails means there will be tail tail head and and head tail head tail and tail tail and tail.

01:12 So the sample space for condition a is going to be sample space of n sa going to be 1, 2, 3, 4, 5, 6, 7, 8.

01:23 So this is 8 and this is equal to sample space of our 3 coins are flipped and that event.

01:29 So this is the sample space of 8.

01:32 So this is equal to this is equal to event as.

01:43 So let's take this as event as so this is equal to event as and so this is sample space of event as.

01:53 So second condition b is given that.

01:55 Let me write that also.

01:56 Second condition is given that there is exactly one head means tail head tail or tail tail head or head tail tail and all are same means tail tail tail tail and head head head.

02:14 So sample space for event b going to be three and two five.

02:18 So sample space of condition b, which is simple space of condition b is equal to five which is not equal to sample space of event as event s is three coins are flipped so sample space of s is equal to eight and this is not equal to five so that means this event is not not a it's not a sample space of sample space of event event s so the third c condition is given by c condition is given so c is given by all fields of are head means head, head, head, and exactly two flips are tails...

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