The six faces of a fair cubical dice are numbered 1, 2, 2, 3, 3, 3. This dice is thrown and then an unbiased coin is thrown the number of times indicated by the score on the dice. Let H denote the no. of heads obtained.

Show that P(H = 2) = 13/48

Question

The six faces of a fair cubical dice are numbered 1, 2, 2, 3, 3, 3. This dice is thrown and then an unbiased coin is thrown the number of times indicated by the score on the dice. Let H denote the no. of heads obtained.

Show that P(H = 2) = 13/48

anonymous · Answer

you could find the probability of throwing tossing two heads for each die roll and add them together and divide by 6
P(2 [1])=0
P(2 [2])=1/4
P(2 [2])=1/4
P(2 [3])= 3/8
P(2 [3])= 3/8
P(2 [3])= 3/8
Sum equals 13/8.  divided by 6 equals 13/48

anonymous · Answer

Why did u divide it by 6 again ?

anonymous · Answer

because we summed the probability 6 possible die rolls.  Your are finding the probability of a single die roll

anonymous · Answer

Likewise you could multiply each of the above probabilities by 1/6, since that is how often you'd expect to roll it.

anonymous · Answer

Got it thx

anonymous · Answer

Aaa sorry last q... Why is it that the probability of P(2 (2)) is 1/4 not 1/2 ?

anonymous · Answer

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4 possibilities, but only 1 has two Heads in it

anonymous · Answer

likewise, if you extend to a third throw there are 3 of 8 outcomes that contain two Heads (don't count the outcome with 3 Heads)

anonymous · Answer

I looked at it all wrong lol thx again

anonymous · Answer

are you more confused now, i can help explain if need be

anonymous · Answer

Nono its very clear ... Thank u very much for ur help