*** A die is rolled 6 times (a) What is the chance of obtaining exactly 1 six? (
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Question
*** A die is rolled 6 times
(a) What is the chance of obtaining exactly 1 six?
(b) What is the chance of obtaining six first and then not six?
(c) What is the chance of obtaining at least 1 six?
*** Complete the following table for the tossing of an unbiased coin. Use the square root law.
Number of tosses
Number of tails
Expected value | SE
Percent of tails
Expected value | SE
100
50 | 2
50% | 2%
2,500
| 0.4%
10,000
1,000,000
Does it confirm the law of averages?
*** You gamble 100 times on the tosse of a coin. If it lands heads, you win $1. If it lands tails, you lose $1. Your net gain will be around ______, give or take _____ or so. Use the box model.
Number of tosses
Number of tails
Expected value | SE
Percent of tails
Expected value | SE
100
50 | 2
50% | 2%
2,500
| 0.4%
10,000
1,000,000
Explanation / Answer
Assuming that the die is fair.
So the probability of obtaining a 6 on any roll of die is 1/6.
Modeling this as a Binomial distribution:
(a)
Probability of obtaining exactly one 6 is:
P = 6C1*p1*(1-p)6-1
Putting values:
P = 6C1*(1/6)1*(1-(1/6))5
Solving we get:
P = 0.402
(b)
Probability of obtaining a 6 on the first roll and not obtaining a 6 in the remaining rolls is:
P = (1/6)*(5/6)5 = 0.067
(c)
Probability of obtaining atleast one 6 = 1 - Probability of not obtaining any 6
Probability of not obtaining any 6 = (5/6)6 = 0.335
So,
Probability of obtaining atleast one 6 = 1-0.335 = 0.665
Hope this helps !
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