Class 10 Maths Probability Numerical

Numerical: A jar contains a red ball, a blue ball and a yellow ball, all the balls being of the same size. What is the probability to takes out the (i) yellow ball? (ii) red ball? (iii) blue ball?

Solution: When you take out a ball, there are 3 possible equally likely outcomes: Red ball, Yellow ball, or Blue ball.

P(Red Ball) = Number of outcomes for Red ball/ Total number of outcomes

Or p(Red Ball) = 1/3

Similarly p(Yellow Ball) = 1/3    & p(Blue ball) = 1/3

Note that p(red Ball)  + p(Yellow Ball) + p(Blue Ball) = 1/3 + 1/3 + 1/3  = 1

Also note that each of these probabilities are in the range 0 ≤ P(E) ≤ 1

Numerical: If P(E) = 0.05, what is the probability of ‘not E’?

Solution:  P(not E) = 1- p(E) = 1 - .05 = .95

Numerical: A die is thrown once. Find the probability of getting  (i) a prime number; (ii) a number lying between 2 and 6; (iii) an odd number

Solution: In a throw of a die, possible outcomes are 1, 2, 3,4, 5,6

Primes numbers in this set are : 2, 3,5

P(prime) = Number of outcomes for Prime/ Total number of outcomes  = 3/6  = ½

Number lying between 2 & 6 are :  3,4, 5

P(Number b/w 2 & 6) = Number of outcomes for number between 2 & 6/ Total number of outcomes  = 3/6  = ½

Odd numbers in the set are: 1, 3, 5

P(Odd Number) = Number of outcomes for odd number / Total number of outcomes  = 3/6  = ½

Numerical: One card is drawn from a well-shuffled deck of 52 cards. Find the probability of getting (i) a king of red colour (ii) a face card (iii) a red face card (iv) the jack of hearts (v) a spade (vi) the queen of diamonds

Solution:  Total number of cards is 52

Number of King of red color card = 2

P(King of red colour) = Number of outcomes for king of red Colour / Total number of outcomes

Or P(King of red colour) = 2/52 = 1/26

Number of face card is 12

P(face card) = Number of outcomes for face card / Total number of outcomes

Or P(face card) = 12/52 = 3/13

Number of Red face card is 12

P(Red face card) = Number of outcomes for Red face card / Total number of outcomes

Or P(Red face card) = 6/52 = 3/26

Number of Jack of Heart is 1

P(Jack of Hearts) = Number of outcomes for jack of Hearts / Total number of outcomes

Or P(Red face card) = 1/52

Number of Spade Card is 13

P(Spade Card) = Number of outcomes Spade Card / Total number of outcomes

Or P(Red face card) = 13/52  = ¼

Number of Queen of Diamonds Card is 1

P(Queen of Diamonds) = Number of outcomes  for Queen of Diamonds / Total number of outcomes

Or P(Red face card) = 1/52

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