document.write( "Question 192152: Q1) Three fair coins are tossed. The number of heads obtained is recorded\r
\n" ); document.write( "\n" ); document.write( "a] Write down a suitable sample space for this experiment\r
\n" ); document.write( "\n" ); document.write( "Let A = \"number of heads equals 2\"
\n" ); document.write( "Let B = \"at least one head is obtained\"\r
\n" ); document.write( "\n" ); document.write( "b] Giving a reason, state whether A and B are mutually exculsive\r
\n" ); document.write( "\n" ); document.write( "c] Calculate P(A) and P(B)\r
\n" ); document.write( "\n" ); document.write( "d] Giving a reason, state whether A and B are independent.\r
\n" ); document.write( "\n" ); document.write( "e] Calculate P (A/B)\r
\n" ); document.write( "\n" ); document.write( "The experiment of tossing three coins is repeated, only this time with three biased coins. Each coin has probability 0.7 of turning up heads. Let the random variable Y denote the number of heads obtained.\r
\n" ); document.write( "\n" ); document.write( "f] Write down the range of Y\r
\n" ); document.write( "\n" ); document.write( "g] For each number k in the range of Y, calculate P(Y = k)
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Algebra.Com's Answer #144320 by stanbon(75887)\"\" \"About 
You can put this solution on YOUR website!
Q1) Three fair coins are tossed. The number of heads obtained is recorded
\n" ); document.write( "a] Write down a suitable sample space for this experiment
\n" ); document.write( "hhh,thh,hth,hht,htt,tht,tth,ttt
\n" ); document.write( "--------------------------------------
\n" ); document.write( "Let A = \"number of heads equals 2\"
\n" ); document.write( "Let B = \"at least one head is obtained\"
\n" ); document.write( "b] Giving a reason, state whether A and B are mutually exculsive
\n" ); document.write( "\"at least one\" included \"two\"
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\n" ); document.write( "c] Calculate P(A)= 3/8
\n" ); document.write( " and P(B) = 7/8
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\n" ); document.write( "d] Giving a reason, state whether A and B are independent.
\n" ); document.write( "P(A)*P(B) = (3/8)(7/9) = 21/64
\n" ); document.write( "P(A and B) = 3/8
\n" ); document.write( "Since they are not equal A and B are not independent.
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\n" ); document.write( "\n" ); document.write( "e] Calculate P (A|B) = P(2 h | at least 1 h) = 3/7
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\n" ); document.write( "The experiment of tossing three coins is repeated, only this time with three biased coins. Each coin has probability 0.7 of turning up heads. Let the random variable Y denote the number of heads obtained.
\n" ); document.write( "f] Write down the range of Y
\n" ); document.write( "0,1,2,3
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\n" ); document.write( "g] For each number k in the range of Y, calculate P(Y = k)
\n" ); document.write( "I'll leave that to you. Remember, each coin is independent.
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\n" ); document.write( "Cheers,
\n" ); document.write( "Stan H.
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