Question

Three dice are rolled and two fair coins are tossed. Let X be the sum of the number of spots that show on the top faces of the dice and the number of coins that land heads up. The expected value of X is ____?

Answer #1

favourable outcome for a digit on dice = 1

and total outcome = 6

So, probability of getting any number of dice = favorable/total = 1/6

Expected value = (sum of numbers)*probability

= (1+2+3+4+5+6)*(1/6)

= 21/6

we have 3 dice, so expected value for 3 dice = 3*E[x]

= 3*21/6

= 63/6

= 10.5

And

Expected value of a single coin = probability of getting heads = 1/2 = 0.5

we have two coins, so expected value of two coins = 2*E[x] = 2*0.5 = 1

therefore, total expected value of X is 10.5+1

**E[x_total]= 11.5**

Three fair dice are rolled. Let X be the total number of spots
showing, that is the sum of the results of the three rolls.
a) Find the probabilities P(X= 3), P(X= 4), P(X= 17), P(X=
18).
b) Find the probability P(X≥ 11).

Three fair coins are tossed. Let x equal be the number of heads
observed. give the probability distribution for x, and find the
mean.

If six fair dice are rolled,
a. On average, what is the sum of the number of spots showing on
top of the 6 dice?
b. What is the probability that all the dice show only ones and
sixes (in any proportion)?

If two fair dice are rolled, what is the probability that the
sum of the numbers rolled is greater than three?

If two fair dice are rolled, find the probability that the sum
of the dice is 7, given that the sum is greater than 6.

1. a pair of fair dice is rolled. if the sum of the spots is 7,
determine the probability that one die showed a 2
2.what is the probability of rolling a sum of seven with a pair
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A pair of dice is rolled. If we let x = sum of the two numbers
that show up on the uppermost face of the dice,
a) determine the probability distribution (mass function) of
x.
b) determine
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2) P(x<6) 6) P(4<x<8)
3) P(x>7) 7) P(x=5)
4) P(x≥3)

Two fair dice are rolled. Find the following probabilities:
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b) P(the sum of the dice is not five)

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a. Find the probability that the sum is 4. b. Find the
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c. Find the probability that the sum is at most 4.

Suppose Brian flips three fair coins, and let X be the number of
heads showing. Suppose Maria flips five fair coins, and let Y be
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.

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