Question

20: There is 70% chance that team A will beat team B, and team C will beat team D. The events are independent. What is the probability that both team A and team C will win?

21: How many 12-digit Hexadecimal numbers end in 55AA? Give your answer as a formula.

Answer 1

20.

P(A win) = 70 % = 0.70

P(C win) = 70 % = 0.70

they are independent

so,

P(A win AND C win) = P(A win)*P(C win)

= 0.70*0.70 = 0.49

P(A win AND C win) = 0.49

21.

if the 12 digit number ends in 55AA so only first 8 digit can vary

in hexadecimal system each digit has 16 choices

so for 8 digits with each having 16 choices

no. of ways = (no. of choices)^(no. of digits - no. of fixed digits) = 16^8 = 4294967296

as a formula : (no. of choices)^(no. of digits - no. of fixed digits) = 16^(12-4)

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