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A locker combination contains four digits. Each digit can be from 0 through 9. What is the probability that a 4-digit combination chosen at random is made up of 4 digits that are all greater than 6 if each digit can be repeated?

1. Find the total number of possible outcomes.
1. (10)(10)(10)(10)
2. Find the number of favorable outcomes.
2. (3)(3)(3)(3)
3. Use the formula
3.
P (event) = Number of favorable outcomes
Number of possible outcomes

User Jim Nutt
by
8.8k points

2 Answers

2 votes

Answer: 81/10,000

Explanation:

Just did it

User Pobrelkey
by
7.9k points
2 votes

Answer:


P=0.0081

Explanation:

We know that the probability of an event is:


P (event) = (Number\ of\ favorable\ outcomes)/(Number\ of\ possible\ outcomes)

Note that between 0 and 9 there are 10 possible digits {0,1,2,3,4,5,6,7,8,9}

If each digit can be repeated and the combination has 4 digits then the number of possible combinations S is:


S = 10 * 10 * 10 * 10 = 10 ^ 4 = 10,000

If all digits obtained must be greater than six, then the possible digits that can be obtained are three: {7,8,9}.

If the combination is 4 digits then the number of results that can be obtained are:


S = 3 * 3 * 3 * 3 = 3 ^ 4 = 81

So:

Number of favorable outcomes = 81

Number of possible outcomes = 10,000

Finally the probability is:


P = (81)/(10,000)\\\\P=0.0081

User Jaspreet Jolly
by
7.4k points

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