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Two dice are thrown simultaneously. If X denotes the number of sixes, then the expectation of X is:
- a)1/3
- b)1/2
- c)1/4
- d)1/6
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
Two dice are thrown simultaneously. If X denotes the number of sixes, ...
Toolbox:
Mean of the probability distribution = ∑(XixP(Xi))
P (X = 1) = P ( 6 on 1st die and no 6 on 2nd OR 6 on 2nd die and no 6 on 1st)
Most Upvoted Answer
Two dice are thrown simultaneously. If X denotes the number of sixes, ...
1/6 expectations of first dice
and
1/6 expectations of seconds dice
than
1/6+1/6= 2/6. or 1/3
and
1/6 expectations of seconds dice
than
1/6+1/6= 2/6. or 1/3
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Community Answer
Two dice are thrown simultaneously. If X denotes the number of sixes, ...
Here, X represents the number of sixes obtained when two dice are thrown simultaneously. Therefore, X can take the value of 0, 1, or 2.
∴ P(X=0)=P(not getting six on any of the dice) = 25/36
P(X=1)=P(sixo n first die and no six on second die) + P(no six on firstdie and six on second die)
=2(1/6 × 5/6)=10/36
P(X=2)=P(sixonboththedice)= 1/36
Therefore, the required probability distribution is as follows.
Then, expectation of X=E(X)=∑Xi
P(Xi)= 0(25/36)+1(10/36)+2(1/36)
= 1/3
∴ P(X=0)=P(not getting six on any of the dice) = 25/36
P(X=1)=P(sixo n first die and no six on second die) + P(no six on firstdie and six on second die)
=2(1/6 × 5/6)=10/36
P(X=2)=P(sixonboththedice)= 1/36
Therefore, the required probability distribution is as follows.
Then, expectation of X=E(X)=∑Xi
P(Xi)= 0(25/36)+1(10/36)+2(1/36)
= 1/3
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Two dice are thrown simultaneously. If X denotes the number of sixes, then the expectation of X is:a)1/3b)1/2c)1/4d)1/6Correct answer is option 'A'. Can you explain this answer?
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