A fair die is rolled seven times. What is the probability that it comes up 5 at least once? Write your answer as a fraction or a decimal, rounded to four decimal places.

0.7209

Step-by-step explanation:

For a fair die, probability of occurrence of any face (including 5) = 1/6.

To determine the probability of having at least one *5" in 7 rolls, the probability distribution formula for occurrence of random variables by combination method is used.

To determine no of occurrence "r" from a total occurrence "n", the probability formula is denoted by:

P(X=r) = nCr × p^r × q^n-r

Where p= probability of success which in this case = 1/6

q = 1-p = 1 - 1/6 = 5/6

To determine the probability of the occurrence of at least one occurrence of "5" from 7 throws, that is P(X≥1), we can determine the probability of occurrence of not having 5 at all and deduct our answer from 1. That is, P(X≥1) = 1 - P(X=0)

When r = 0,

P(X=0) = 7C0 × (1/6)^0 × (5/6)^7 = 0.2791

Hence, P(X≥1) = 1 - 0.2791 = 0.7209

i used to know how to do this in 7th but i forget easily

step-by-step explanation:

7. d. 64

8. i. 32

9. c. 125

10. j. none of the above

11. d. 81

12. i. 216

13. e. none of the above

14. g. 240

15. e. none of the above

16. g. 32

17.   e. none of the above