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Re: Rolling a four-sided dice, what is the probability of roll..
[#permalink]
15 Oct 2022, 10:30
Given that we are Rolling a four-sided dice and We need to find what is the probability of rolling a 4 three times out of four?
As we are rolling a four sides dice four times => Number of cases = \(4^4\)
To get 4 three times out of 4 let's find out those three places out of 4 where 4 will come. This can be done in 4C3 ways => \(\frac{4!}{3!*1!}\) = 4 ways
Now, those 3 4's can occupy those places in 1 way each (As there is only one 4 out of 4)
The fourth roll can take any value except 4 => 3 ways (1, 2, 3)
=> Total ways = 4 * 1 * 1 * 1 * 3 = 12 ways
=> Probability of rolling a 4 three times out of four = \(\frac{12}{4^4}\) = \(\frac{3}{64}\)
So, Answer will be E Hope it helps!
Watch the following video to learn How to Solve Dice Rolling Probability Problems
gmatclubot
Re: Rolling a four-sided dice, what is the probability of roll.. [#permalink]