Question

Four dice are thrown simultaneously.Find the number of ourcomes in which at least oone is 3

Answer 1

Hi there!
Here's the answer:

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First identify keyterm 'atleast one'

¶¶¶ (atleast one outcome satisfying E) = (Total outcomes) - (none of outcome satisfying E)

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Total outcomes when 4 dice are rolled simultaneously.
T= 6⁴ = 1296.

E be Event that at least one 3 exists in S.

Now,
• None of outcome satisfying E
= Except showing 3 on dice, dice can show all other possible No.s.

• When 1 outcome is eliminated from 6 possible cases (1,2,3…,6) for a single die,
we are having now 5 possible outcomes for a single die

• As 4 dice are rolled, we have N= 5⁴= 625 possible outcomes for None of outcome satisfying E

•°• Required No. of outcomes = T - N
= 1296 - 625 = 671.