Question: The access code for a car\'s security system consists of five digits.

Question

Question: The access code for a car's security system consists of five digits. The first digit cannot be 4 and the last digit must be even. How many different codes are available?

The number of different codes available is _______?

Question: 34% of a certain country's voters think that it is too easy to vote in their country. You randomly select 12 likely voters. Find the probability that the number of likely voters who think that it is too easy to vote is (a) exactly three, (b) at least four, (c) less than eight.

(a) P(3)=_____ (Round to three decimal places as needed.)

(b) P(x4)=_____ (Round to three decimal places as needed.)

(c) P(x<8)=_____ (Round to three decimal places as needed.)

Explanation / Answer

1) first digit can be filled by 9 ways

second, third and fourth digit can be filled by 10 * 10 * 10 = 1000 ways

fifth digit can be filled by 4 ways

The number of different codes available = 9 * 1000 * 4 = 36000

2) p = 0.34

n = 12

P(X = x) = 12Cx * 0.34x * (1 - 0.34)12-x

a) P(X = 3) = 12C3 * 0.343 * 0.669 = 0.2055

b) P(X > 4) = 1 - P(X < 4)

                   = 1 - (P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3))

                   = 1 - (12C0 * 0.340 * 0.6612 + 12C1 * 0.341 * 0.6611 + 12C2 * 0.342 * 0.6610 + 12C3 * 0.343 * 0.669 )

                   = 1 - 0.3742

                   = 0.6258

c) P(X < 8) = 1 - [P(X = 8) + P(X = 9) + P(X = 10) + P(X = 11) + P(X = 12)]

                  = 1 - [12C8 * 0.348 * 0.664 + 12C9 * 0.349 * 0.663 + 12C10 * 0.3410 * 0.662 + 12C11 * 0.3411 * 0.661 + 12C12 * 0.3412 * 0.660 ]

                  = 1 - 0.0213

                  = 0.9787

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