The sample space for three subsequent tosses of a fair coin is given as S = {hhh, hht, hth, htt, thh, tht, tth, ttt}. Define events, A: at least one tail is observed, and B: more tails than heads is observed. Find A ∩ B.

a.{htt, tht, tth, ttt}b.{hht, hth, htt, thh, tht, tth, ttt} c.{hhh, hht, hth, thh} d.{hhh, hht, hth, htt, thh, tht, tth, ttt} e.{hhh, ttt}

The sample space for three subsequent tosses of a fair coin is S = {hhh, hht, hth, htt, thh, tht, tth, ttt}. Define events, A: at least one tail is observed, and B: more tails than heads is observed. Find A ∩ Bc.

a.{htt, tht, tth, ttt} b.{hht, hth, thh} c.{hhh, hht, hth, thh} d.{hhh, hht, hth, htt, thh, tht, tth, ttt} e.{hhh, ttt}

1. Option A. {htt, tht, tth, ttt}

2. Option B. {hht, hth, thh}

Step-by-step explanation:

1. S = {hhh, hht, hth, htt, thh, tht, tth, ttt}.

A: At least one tail means one tail and above. This is illustrated below:

A = {hht, hth, htt, thh, tht, tth, ttt}

B: more tails than heads is observed means the tails must be more than the heads. This is illustrated below:

B = {htt, tht, tth, ttt}

A ∩ B: This simply means elements common to both A and B. This is illustrated below:

A ∩ B = {htt, tht, tth, ttt}

2. S = {hhh, hht, hth, htt, thh, tht, tth, ttt}.

A: At least one tail means one tail and above. This is illustrated below:

A = {hht, hth, htt, thh, tht, tth, ttt}

B: more tails than heads is observed means the tails must be more than the heads. This is illustrated below:

B = {htt, tht, tth, ttt}

Bc: This is the set of elements found in the universal set but not found in the set B

Bc = { hhh, hht, hth, thh}

AnBc: means elements common to both set. This is illustrated below:

AnBc = {hht, hth, thh}

i use my brain for prombles like this maybe you could try it

step-by-step explanation:

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