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
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
c] Calculate P(A) and P(B)
d] Giving a reason, state whether A and B are independent.
e] Calculate P (A/B)
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
g] For each number k in the range of Y, calculate P(Y = k)
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! 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.
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