Solve every problem correctly for full points! If 3 balls are drawn from a bag c

Question

Solve every problem correctly for full points!

If 3 balls are drawn from a bag containing 3 red and 4 blue balls, what is the expected number of red balls in the sample? If a license plate consists of four digits, how many different licenses could be created having at least one digit repeated licenses licenses licenses licenses licenses How many 3-digit numbers can be formed using the digits 0. 1. 2. 3. 4. 5. 6. if repetitions are not allowed? digit numbers three-digit numbers three-digit numbers three-digit numbers

Explanation / Answer

14. Total no of combinations = 7C3 = 35

Prob of 0 red balls = 4C3/35 = 4/35

Prob of 1 red balls = 3C1*4C2/35 = 3*6/35 = 18/35

Prob of 2 red balls = 3C2*4C1/35 = 3*4/35 = 12/35

Prob of 3 red balls = 1/35

So expected number of red balls = 0*4/35 + 1*18/35 + 2*12/35 + 3*1/35 = 45/35 = 9/7 = 1.2857 red balls

15. Total no of combinations with no conditions = 10^4 = 10,000

No of combinations with no digit repeated = 10*9*8*7 = 5040

So no of combinations with atleast one digit repeated = 10,000-5040 = 4,960

16. Total no of combinations with no conditions = (26^2)*(10^4) = 6,760,000

No of combinations with no digit or letter repeated = (26*25)*(10*9*8*7) = 3,276,000

So no of combinations with atleast one digit or letter repeated = 6,760,000-3,276,000 = 3,484,000

17. No of selections for first digit = 6 (all 7 numbers except zero)

No of selections for second digit = 6 (all 7 numbers except the number chosen for first digit)

No of selections for third digit = 5 (all 7 numbers except the numbers chosen for first digit and second digit)

So total no of selections = 6*6*5 = 180 different numbers

Hope this helped ! Let me know in case of any queries.

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