A card picked at random from a packed a \(52\) playing cards. Find the probability that it is a Ace or King?
\(\frac{3}{12}\)
\(\frac{12}{3}\)
\(\frac{2}{13}\)
\(\frac{13}{2}\)
Answer: (c) \(\frac{2}{13}\)Solution: total number of possible outcomes = \(52\)number of favourable outcomes = \(8\), then $$ Probability = \frac{8}{52} $$ $$ = \frac{2}{13} $$
A bag contains \(8\) white and \(9\) black balls, if two balls are drawn at random what is the probability that both are white?
\(\frac{7}{34}\)
\(\frac{5}{34}\)
\(\frac{5}{27}\)
\(\frac{7}{27}\)
Answer: (a) \(\frac{7}{34}\)Solution: number of white balls = \(8\)number of black balls = \(9\), then $$ Probability = \frac{^8C_2}{^{17}C_2} $$ $$ = \frac{28}{136} = \frac{7}{34} $$
If four coins are tossed, then find the probability of getting atleast one tail?
\(\frac{16}{15}\)
\(\frac{15}{16}\)
\(\frac{12}{13}\)
\(\frac{13}{12}\)
Answer: (b) \(\frac{15}{16}\)Solution: total number of events = \(2^4\) = \(16\)probability that no tail occurs = \(\frac{1}{16}\)probability that atleast one tail occurs, $$ P = 1 - \frac{1}{16} = \frac{15}{16} $$
If a fair dice is thrown, then find the probability of getting a number greater than four?
\(\frac{1}{2}\)
\(\frac{1}{3}\)
\(\frac{1}{4}\)
\(\frac{1}{5}\)
Answer: (b) \(\frac{1}{3}\)Solution: number of possible outcomes = \(6\)number of favourable events = \(\{5, \ 6\}\)number of favourable outcomes = \(2\), then $$ Probability = \frac{2}{6} $$ $$ = \frac{1}{3} $$
If a number is drawn from the numbers between \(1\) to \(20\), then find the probability of getting a number multiple of \(4\)?
\(\frac{1}{2}\)
\(\frac{1}{3}\)
\(\frac{1}{4}\)
\(\frac{1}{5}\)
Answer: (c) \(\frac{1}{4}\)Solution: number of possible outcomes = \(20\)number of favourable events = \(\{4, \ 8, \ 12, \ 16, \ 20\}\)number of favourable outcomes = \(5\), then $$ Probability = \frac{5}{20} $$ $$ = \frac{1}{4} $$
If a number is drawn from the numbers between \(1\) to \(10\), then find the probability of getting a number multiple of \(3\)?
\(\frac{3}{10}\)
\(\frac{2}{9}\)
\(\frac{3}{13}\)
\(\frac{4}{13}\)
Answer: (a) \(\frac{3}{10}\)Solution: number of possible outcomes = \(10\)number of favourable events = \(\{3, \ 6, \ 9\}\)number of favourable outcomes = \(3\), then $$ Probability = \frac{3}{10} $$
A card is drawn from the \(52\) playing cards. Find the probability of getting a heart?
\(\frac{1}{2}\)
\(\frac{1}{3}\)
\(\frac{1}{4}\)
\(\frac{1}{5}\)
Answer: (c) \(\frac{1}{4}\)Solution: number of favourable outcomes = \(13\)number of possible outcomes = \(52\), then $$ Probability = \frac{13}{52} $$ $$ = \frac{1}{4} $$
A card is drawn from the \(52\) playing cards. Find the probability of black colour king?
\(\frac{1}{16}\)
\(\frac{1}{21}\)
\(\frac{1}{13}\)
\(\frac{1}{26}\)
Answer: (d) \(\frac{1}{26}\)Solution: number of favourable outcomes = \(2\)number of possible outcomes = \(52\), then $$ Probability = \frac{2}{52} $$ $$ = \frac{1}{26} $$
If probability of A to win a game is \(\frac{5}{7}\) and probability of B to win the game is \(\frac{3}{5}\), then find the probability that eather A or B win the game?
\(\frac{45}{46}\)
\(\frac{46}{45}\)
\(\frac{46}{35}\)
\(\frac{35}{46}\)
Answer: (c) \(\frac{46}{35}\)Solution: probability of A to win the game P(A) = \(\frac{5}{7}\)probability of B to win the game P(B) = \(\frac{3}{5}\), then $$ P = P \ (A) + P \ (B) $$ $$ P = \frac{5}{7} + \frac{3}{5} $$ $$ = \frac{46}{35} $$
If probability of x to pass an exam is \(\frac{1}{5}\) and probability of y to pass the exam is \(\frac{1}{3}\), then find the probability that nobody will pass the exam?
\(\frac{14}{15}\)
\(\frac{15}{14}\)
\(\frac{12}{13}\)
\(\frac{13}{12}\)
Answer: (a) \(\frac{14}{15}\)Solution: probability of x to pass the exam P(x) = \(\frac{1}{5}\)probability of y to pass the exam P(y) = \(\frac{1}{3}\)then probability that both of them will pass the exam $$ P = P \ (x) \times P \ (y) $$ $$ P = \frac{1}{5} \times \frac{1}{3} $$ $$ = \frac{1}{15} $$ now the probability that nobody will pass the exam, $$ = 1 - \frac{1}{15} = \frac{14}{15} $$