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This is one of our many quizzes on Probability. Click on this to access more such competitive quizzes on Algebra.

Probability Quiz 2

mathematics

 What is the probability of picking a club card if three club cards are lost from the deck of cards?

 Apply the formula of probability and calculate the number of cards in the deck.

  $\text{Total cards} = 52$$\text{Lost cards} = 3$$\text{Remaining cards} = 52 - 3 = 49$$\text{Remaining club cards} = 13 - 3 = 10$$\text{Probability} = \dfrac{\text{No. of favourable outcomes}}{\text{Total outcomes}} = \dfrac{{10}}{{49}}$

 Find the number of cases if a coin is tossed five times is

 To calculate the number of cases for tossing a coin is ${2^n}$.

  Number of cases in tossing a coin $ = {2^n}$ $ \\ $ $n $= no. of times coin tossed $ \\ $ Here $n = 5$ $ \\ $ No. of cases $ = {2^n} = {2^5} = 32$ $ \\ $ Hence, the number of cases $ = 32$.

 Evaluate the probability of getting 2 face card of spade if two cards are drawn from deck of 52 cards: 

 To find the probability of 2 cards, you need to multiply the probability of the first card and the second card.

Total cards $ = 52$ $ \\ $ Number of spades $ = 13$ $ \\ $ Number of face card of spade $ = 3$ $ \\ $ Probability $($2 face card of spade$)$ $ \\ $ $\Rightarrow$ P$($First card is face card of spade$) \times $ P$($Second card is face card of spade$)$ $ \\ \Rightarrow \dfrac{3}{{52}} \times \dfrac{2}{{51}}   \\   \Rightarrow \dfrac{1}{{26}} \times \dfrac{1}{{17}}   \\   \Rightarrow \dfrac{1}{{442}}   \\ $ Hence, P$($2 face cards of spade$) = \dfrac{1}{{442}}$.

 25 apples are marked with the number 1 to 25. Sunita will buy the apple with composite numbers marked on it, then what is the probability that she will not buy apples?

 Sunita will not buy the apples with prime numbers on it, so find the probability of prime numbers. 

 Total apples $ = 25$ $ \\ $ Cases of prime number $ = 2,3,5,7,11,13,17,19,23$ $ \\ $ No. of prime number $ = 9$ $ \\ $ P$($Sunita will not buy apples$)$ $ \Rightarrow \dfrac{\text{No. Of favourable outcomes}}{\text{total outcomes}}   \\   \Rightarrow \dfrac{9}{{25}}   \\  $

 Evaluate the total number of cases if a dice is thrown thrice.

 Formula to calculate the total number of cases in case of dice is $6^n$.

 Number of cases of dice $ = {6^n}$ $ \\ $ $n =$ number of times dice is thrown $ \\ $ Here $n = 3$ $ \\ \text{No. of cases} = {6^n}   \\   \Rightarrow {6^3}   \\   \Rightarrow 216   \\  $ Number of cases of dice thrown three times is 216.