Solution: \[\left( v \right)\] Number of favorable outcomes for a diamond or a spade \[=\text{ }13\text{ }+\text{ }13\text{ }=\text{ }26\] So, number of favorable outcomes \[=\text{ }26\] Hence,...

Solution: \[\left( iii \right)\] Favorable outcomes for jack or queen of hearts \[=\text{ }1\text{ }jack\text{ }+\text{ }1\text{ }queen\] So, the number of favorable outcomes \[=\text{ }2\] Hence,...

Solution: We have, Total possible outcomes \[=\text{ }52\] \[\left( i \right)\]Number queens of red color \[=\text{ }2\] Number of favorable outcomes\[~=\text{ }2\] Hence, P(queen of red color)...

Solution: \[\left( v \right)\] Favorable outcomes for a number less than or equal to \[9\text{ }are\text{ }1,\text{ }2,\text{ }3,\text{ }4,\text{ }5,\text{ }6,\text{ }7,\text{ }8,\text{ }9\] So,...

Solution: \[\left( iii \right)\]Favorable outcomes for a prime number are \[2,\text{ }3,\text{ }5,\text{ }7,\text{ }11\] So, number of favorable outcomes\[~=\text{ }5\] Hence, P(the pointer will be...

Solution: We have, Total number of possible outcomes \[=\text{ }12\] \[\left( i \right)\] Number of favorable outcomes for \[6\text{ }=\text{ }1\]6 Hence, \[P\left( the\text{ }pointer\text{...

Solution: \[\left( iii \right)\] Number of favourable outcomes for neither Re \[1\]nor Rs \[5\]coins \[=\] Number of favourable outcomes for Rs\[~2\] coins \[=\text{ }50\text{ }=\text{ }n\left( E...

Solution: We have, Total number of coins \[=\text{ }20\text{ }+\text{ }50\text{ }+\text{ }30\text{ }=\text{ }100\] So, the total possible outcomes \[=\text{ }100\text{ }=\text{ }n\left( S \right)\]...

Solution: \[\left( iii \right)\] Number of favorable outcomes for white or green ball \[=\text{ }16\text{ }+\text{ }8\text{ }=\text{ }24\text{ }=\text{ }n\left( E \right)\] Hence, probability for...

Solution: Total number of possible outcomes \[=\text{ }10\text{ }+\text{ }16\text{ }+\text{ }8\text{ }=\text{ }34\] balls So, \[n\left( S \right)\text{ }=\text{ }34\] \[\left( i \right)\] Favorable...

Solution: We know that, P(do not have the same birthday) \[+\]P(have same birthday) \[=\text{ }1\] \[0.897\text{ }+\] P(have same birthday) \[=\text{ }1\] Thus, P(have same birthday) \[=\text{...

Solution: We have, Total possible outcomes = number of red balls. \[\left( i \right)\] Number of favourable outcomes for black balls \[=\text{ }0\] Hence\[,\text{ }P\left( black\text{ }ball...

Solution: We know that, \[P\left( E \right)\text{ }+\text{ }P\left( not\text{ }E \right)\text{ }=\text{ }1\] So, \[0.59\text{ }+\text{ }P\left( not\text{ }E \right)\text{ }=\text{ }1\] Hence,...

Solution \[\left( iii \right)\text{ }As\text{ }0\text{ }\le \text{ }37\text{ }%\text{ }=\text{ }\left( 37/100 \right)\text{ }\le \text{ }1\] Thus, \[37\text{ }%\] can be a probability of an event....

Solution: We know that probability of an event E is \[0\text{ }\le \text{ }P\left( E \right)\text{ }\le \text{ }1\] \[\left( i \right)\text{ }As\text{ }0\text{ }\le \text{ }3/7\text{ }\le \text{...

Solution: \[\left( iii \right)\] All the outcomes are favourable to the event \[E\text{ }=\]‘sum of two numbers \[\le ~12\] Thus, \[P\left( E \right)\text{ }=\text{ }n\left( E \right)/\text{...

Solution: We have, the number of possible outcomes \[=\text{ }6~\times \text{ }6\text{ }=\text{ }36\] \[\left( i \right)\] The outcomes favourable to the event ‘the sum of the two numbers is...

Solution: We have, Total number of shirts \[=\text{ }50\] Total number of elementary events \[=\text{ }50\text{ }=\text{ }n\left( S \right)\] \[\left( i \right)\] As, trader accepts only good shirts...

Solution: Total result \[=\text{ }0\text{ }sec\text{ }to\text{ }40\text{ }sec\] Total possible outcomes \[=\text{ }40\] So\[,\text{ }n\left( S \right)\text{ }=\text{ }40\] Favourable results...

Solution: \[\left( iii \right)\] Number of black cards left \[=\text{ }23\text{ }cards\text{ }\left( 13\text{ }club\text{ }+\text{ }10\text{ }spade \right)\] Event of drawing a black card \[=\text{...

Solution: We have, Total number of cards \[=\text{ }52\] If \[3\] face cards of spades are removed Then, the remaining cards \[=\text{ }52\text{ }\text{ }3\text{ }=\text{ }49\text{ }=\] number of...

Solution: We have, Total number of balls in the box \[=\text{ }7\text{ }+\text{ }8\text{ }+\text{ }5\text{ }=\text{ }20\] balls Total possible outcomes \[=\text{ }20\text{ }=\text{ }n\left( S...

Solution: We know that, When two coins are tossed simultaneously, the possible outcomes are \[\left\{ \left( H,\text{ }H \right),\text{ }\left( H,\text{ }T \right),\text{ }\left( T,\text{ }H...

Solution: Out of the two friends, A’s birthday can be any day of the year. Now, B’s birthday can also be any day of \[365\] days in the year. We assume that these \[365\] outcomes are equally...

Solution: \[\left( i \right)\]We know that, The probability of winning of A \[+\]Probability of losing of A \[=\text{ }1\] And, Probability of losing of A \[=\] Probability of winning of B...

Solution: \[\left( v \right)\] Numbers less than \[8\text{ }=\text{ }\left\{ \text{ }2,\text{ }3,\text{ }4,\text{ }5,\text{ }6,\text{ }7 \right\}\]\[\] Event of drawing a card with number less than...

  Solution: \[\left( iii \right)\] Event of drawing a queen of black colour \[=\text{ }\left\{ Q\left( spade \right),\text{ }Q\left( club \right) \right\}\text{ }=\text{ }E\] So,\[~n\left( E...

Solution: We have, the total number of possible outcomes \[=\text{ }52\] So, \[n\left( S \right)\text{ }=\text{ }52\] \[\left( i \right)~\]No. of face cards in a deck of \[52\]cards \[=\text{...

Solution: The number of possible outcomes when dice is thrown \[=\text{ }\left\{ 1,\text{ }2,\text{ }3,\text{ }4,\text{ }5,\text{ }6 \right\}\] So\[,\text{ }n\left( S \right)\text{ }=\text{ }6\]...

Solution: \[\left( iii \right)\] Probability of not drawing a yellow ball \[=\text{ }1\text{ }\] Probability of drawing a yellow ball Thus, probability of not drawing a yellow ball \[=\text{...

Solution: The total number of balls in the bag \[=\text{ }3\text{ }+\text{ }4\text{ }+\text{ }1\text{ }=\text{ }8\] balls So, the number of possible outcomes \[=\text{ }8\text{ }=\text{ }n\left( S...

Solution: \[\left( iii \right)\] E = event of getting both heads or both tails \[=\text{ }\left\{ HH,\text{ }TT \right\}\] \[n\left( E \right)\text{ }=\text{ }2\] Hence, probability of getting both...

Solution: We know that, when two coins are tossed together possible number of outcomes = {HH, TH, HT, TT} So, \[n\left( S \right)\text{ }=\text{ }4\] \[\left( i \right)\]E = event of getting both...

Solution: In throwing a dice, total possible outcomes \[=\text{ }\left\{ 1,\text{ }2,\text{ }3,\text{ }4,\text{ }5,\text{ }6 \right\}\] So\[,\text{ }n\left( S \right)\text{ }=\text{ }6\] For two...

Solution: We know that, Number of pages in the book \[=\text{ }85\] Number of possible outcomes \[=\text{ }n\left( S \right)\text{ }=\text{ }85\] Out of \[85\]pages, pages that sum up to \[8\text{...

Solution: \[\left( iii \right)\] On a dice, numbers less than \[8\text{ }=\text{ }\left\{ 1,\text{ }2,\text{ }3,\text{ }4,\text{ }5,\text{ }6 \right\}\] So\[,\text{ }n\left( E \right)\text{ }=\text{...

Solution: We know that, In throwing a dice, total possible outcomes \[=\text{ }\left\{ 1,\text{ }2,\text{ }3,\text{ }4,\text{ }5,\text{ }6 \right\}\] So\[,\text{ }n\left( S \right)\text{ }=\text{...

Solution: \[\left( iii \right)\] From numbers \[1\text{ }to\text{ }25\], there is only one number which is multiple of \[3\text{ }and\text{ }5\text{ }i.e.~\left\{ 15 \right\}\] So, favorable number...

Solution: We know that, there are \[25\] cards from which one card is drawn. So, the total number of elementary events \[=\text{ }n\left( S \right)\text{ }=\text{ }25\] \[\left( i \right)\]From...

Solution: \[\left( v \right)\]From numbers \[1\text{ }to\text{ }100\], there are \[47\] numbers which are less than \[48\text{ }i.e.~\{1,\text{ }2,\text{ }\ldots \ldots \ldots ..,\]\[46,\text{...

Solution: \[\left( iii \right)\] From numbers \[1\text{ }to\text{ }100\], there are \[19\] numbers which are between \[40\text{ }and\text{ }60\text{ }i.e.~\{41,\text{ }42\], \[43,\text{ }44,\text{...

Solution: We kwon that, there are \[100\] cards from which one card is drawn. Total number of elementary events \[=\text{ }n\left( S \right)\text{ }=\text{ }100\] \[\left( i \right)~\] From numbers...

Solution: \[\left( iii \right)\] From numbers \[2\text{ }to\text{ }10\], there is one number which is an even number as well as multiple of \[3\text{ }i.e.\text{ }6\] So, favorable number of events...

Solution: We know that, there are totally \[9\] cards from which one card is drawn. Total number of elementary events \[=\text{ }n\left( S \right)\text{ }=\text{ }9\] \[\left( i \right)\] From...

Solution: \[\left( i \right)\] Winning of Geeta is a complementary event to winning of Ritu Thus, P(winning of Ritu) \[+\]P(winning of Geeta) \[=\text{ }1\] P(winning of Geeta) \[=\text{ }1\text{...

Solution: \[\left( i \right)\] Two complementary events, taken together, include all the outcomes for an experiment and the sum of the probabilities of all outcomes is \[1.\]...

Solution: \[\left( v \right)\]There are \[26\] red cards in a deck, and \[6\] of these cards are face cards (\[2\] kings, \[2\]queens and \[2\]jacks). The number of favourable outcomes for the event...

Solution: \[\left( iii \right)\] Number of red cards in a deck \[=\text{ }26\] The number of favourable outcomes for the event of drawing a red card \[=\text{ }26\] Then, probability of drawing a...

Solution: We know that, Total number of cards \[=\text{ }52\] So, the total number of outcomes \[=\text{ }52\] There are \[13\] cards of each type. The cards of heart and diamond are red in colour....

Solution: Here, the sample space \[=\text{ }\left\{ 1,\text{ }2,\text{ }3,\text{ }4,\text{ }5,\text{ }6 \right\}\] \[n\left( s \right)\text{ }=\text{ }6\] \[\left( i \right)\] If \[E\text{ }=\]event...

Solution: Here, the sample space \[=\text{ }\left\{ 1,\text{ }2,\text{ }3,\text{ }4,\text{ }5,\text{ }6 \right\}\] So\[,\text{ }n\text{ }\left( s \right)\text{ }=\text{ }6\] \[\left( i \right)\]If...