Question

Tomer is playing a game that involves rolling 5 6-sided dice at once, and his goal is to roll the dice so exactly 4 of them land showing a "1

Which of the following would find the probability that exactly 4 of the 5 dice land showing a "1"?
Choose 1 answer:
a
b
c
d
e

Answer 1

The probability of rolling exactly 4 out of 5 six-sided dice and getting a "1" on each is found using the binomial probability formula and is approximately 0.0032.

Step-by-step explanation:

To calculate the probability that exactly 4 of the 5 dice land showing a "1", we can use the binomial probability formula. The binomial probability formula is given by:

P(X = k) = (n choose k) · (p)^k · (1-p)^(n-k)

where:

• n is the number of trials (in this case, 5)
• k is the number of successes we want (in this case, 4)
• p is the probability of success on a single trial (for a die, the probability of rolling a "1" is 1/6)
• (1-p) is the probability of failure on a single trial (the probability of not rolling a "1")

Using this formula, we can calculate:

P(X = 4) = (5 choose 4) · (1/6)^4 · (5/6)

Here, (5 choose 4) represents the number of ways we can choose which 4 of the 5 dice will show a "1", which is 5. Thus, the calculation becomes:

P(X = 4) = 5 · (1/6)^4 · (5/6) = 5 · (1/1296) · (5/6) = (5 · 5) / (1296 · 6)

P(X = 4) = 25 / 7776 = 0.003215 (approximately, rounded to six decimal places)

Therefore, the probability of rolling exactly 4 out of 5 dice showing a "1" is approximately 0.0032.