Loretta is rolling an unfair 6-sided die with a single number between 1 and 6 on each face. She has a 70% chance of rolling a four. She is playing a game with a friend and knows that if she rolls a four on three of her next five rolls she will lose the game. She wants to determine the probability that she rolls a four on three of her next five rolls.
Loretta sets up her simulation using a table of random digits between 0 and 9. She let 0-6 represent rolling a four and 7-9 represent not rolling a four. She selects five digits.
She performs the simulation 18 times and records her results in the table. What is the probability that Loretta rolls a four on 3 of 5 rolls?
A. 1/18
B. 1/6
C. 5/6
D. 17/18
To determine the probability that Loretta rolls a four on 3 of 5 rolls, we can use the binomial probability formula:
P(X=k) = (n choose k) * p^k * (1-p)^(n-k)
Where:
n = total number of rolls = 5
k = number of successful rolls (rolling a four) = 3
p = probability of rolling a four on a single roll = 0.7
Plugging in the values into the formula:
P(X=3) = (5 choose 3) * 0.7^3 * (1-0.7)^(5-3)
P(X=3) = (10) * 0.343 * 0.09
P(X=3) = 0.3087
Therefore, the probability that Loretta rolls a four on 3 of 5 rolls is approximately 0.3087, which is closest to option C. 5/6.