If a die is rolled 40 times, there are 6 <mrow class="MJX-TeXAtom-ORD">

Davon Irwin

Davon Irwin

Answered question

2022-06-15

If a die is rolled 40 times, there are 6 40 different sequences possible. What fraction of these sequences have exactly 22 numbers less than or equal to 3?

Answer & Explanation

Odin Jacobson

Odin Jacobson

Beginner2022-06-16Added 17 answers

Total possible outcomes = 6 40
Sequence has 22 numbers less that equal to 3. Then, probabilities of these 22 positions are 1, 2 or 3 and remaining 18 positions are 4, 5 and 6.
Total favourable cases
= 3 22 × 3 18 = 3 40
Then, = 3 40 6 40 = 3 40 3 40 × 3 40 = 1 2 40
= 9.094947 × 10 13

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