Question

QUESTION 01. Two roads, Broadway and State, connect the towns of East-land and Harping. Three roads, Park, Fairvew, and Main, connect the towns of Harping and Johnstown. Find the number of possible routs from East-land to Johnstown that pass through Harping. Then find the probability that State and Fairvew will be used if a rout is selected at random. State the probability as a fraction and percent and its likelihood.

QUESTION 2. Find the number of possible choices for a 2-digit password that is greater than 19. Then find the number of possible choices for a 4-digit Personal Identification Number (PIN) if the digits cannot be repeated.

QUESTION 3. Determine the number of possible of outcomes when tossing one coin, two coins, and three coins. Then determine the number of possible outcomes for tossing 'n' coins. Explain your reasoning.

PS: Please answer i'm tiring to study but can get these three :(

Answer 1

Problem #6160 Two roads, Broadway and State, connect the towns of East-land and Harping. Three roads, Park, Fairvew, and Main, connect the towns of Harping and Johnstown. Find the number of possible routs from East-land to Johnstown that pass through Harping. Then find the probability that State and Fairvew will be used if a rout is selected at random. State the probability as a fraction and percent and its likelihood.

Solution Due to combinatorial rule of product: “ if we have $a$ ways of doing something and $b$ ways of doing another thing, then there are $a\cdot b$ ways of performing both actions” the number of possible routs from East-land to Johnstown is $2\cdot 3=6$. Thus, the probability of choosing any route(under the assumption of selecting at random, that is with equal probabilities) is $1/6\approx 0.166$. Hence, the probability that our route is State—Fairvew is $1/6$ as any other of the possible ways.

Note, that the probability that one will use State is $3/6=1/2$, and the probability that one will use Fairvew is $2/6=1/3$.

Answer $1/6$ or $0.166$ or $16\%$ or $1:6$.

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