A ten sided die is numbered from one to ten. What is the probability of rolling a four on 3 consecutive rolls

Question

A ten sided die is numbered from one to ten. What is the probability of rolling a four on 3 consecutive rolls

Answer 1

probability of a 4 on one roll is 1/10 = 10%

probability of 4 three times on 3 rolls = (1/10)^3 = 1/1000 = 0.1%

or if you meant what's the chance of at least one 4 on 3 rolls

3(1/10(9/10)(9/10) + 3(1/10)(1/10)(9/10) + (1/10)(1/10)(1/10)

= 243/1000 + 27/1000 + 1/1000 = 271/1000 = 27.1% probability of at least one 4 in 3 rolls

3 ways to get one 4 in 3 rolls. the 4 could come up on the 1st, 2nd or 3rd roll

3 ways to get two 4's in 3 rolls, the 2 4's could come up 1st & 2nd, 1st & 3rd or 2nd & 3rd rolls

only 1 way to get all 4's

add the probabilities up.

or if you meant to ask what's the probability of exactly one 4 in 3 rolls

that's 243/1000 = 24.3% chance