JEE Main · 2020 · 05 Sep 2020 · Shift 1 · Probability

Four fair dice are thrown independently 27 times. Then the expected number of times, at least two dice show up a three or a five, is ______.

Answer: 11

Solution

For a single die the chance of showing a three or a five is

\frac{2}{6} = \frac{1}{3}

. For four dice the probability that at least two show a three or a five is

(2 4) (\frac{1}{3})^{2} (\frac{2}{3})^{2} + (3 4) (\frac{1}{3})^{3} (\frac{2}{3}) + (4 4) (\frac{1}{3})^{4} = \frac{24 + 8 + 1}{81} = \frac{33}{81} = \frac{11}{27}

. Over

27

independent throws the expected number of such outcomes is

27 \times \frac{11}{27} = 11

JEE Main · 2020 · 05 Sep 2020 · Shift 1 · Integer answer