Question 192152
Q1) Three fair coins are tossed. The number of heads obtained is recorded 
a] Write down a suitable sample space for this experiment
hhh,thh,hth,hht,htt,tht,tth,ttt
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Let A = "number of heads equals 2"
Let B = "at least one head is obtained" 
b] Giving a reason, state whether A and B are mutually exculsive 
"at least one" included "two"
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c] Calculate P(A)= 3/8
 and P(B) = 7/8
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d] Giving a reason, state whether A and B are independent.
P(A)*P(B) = (3/8)(7/9) = 21/64 
P(A and B) = 3/8
Since they are not equal A and B are not independent.
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e] Calculate P (A|B) = P(2 h | at least 1 h) = 3/7
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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. 
f] Write down the range of Y 
0,1,2,3
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g] For each number k in the range of Y, calculate P(Y = k)
I'll leave that to you.  Remember, each coin is independent.
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Cheers,
Stan H.