# PRACTICE QUESTIONS ON PROBABILITY FOR GRADE 11

Question 1 :

If two coins are tossed simultaneously, then find the probability of getting (i) one head and one tail (ii) at most two tails

Solution :

Sample space  =  { HH, HT, TH, TT }

n(S)  =  4

(i) one head and one tail

Let "A" be the event of getting the probability of one head and one tail.

A  =  {HT, TH}

n(A)  =  2

P(A)  =  n(A) / n(S)

=  2/4  ==>  1/2

(ii) at most two tails

Let "B" be the event of getting the probability of at most two tails.

At most two tails means, we may get 0 tail, 1 tail and 2 tails.

B  =  { HH, HT, TH, TT }

n(B)  =  4

P(B)  =  n(B) / n(S)

=  4/4  ==>  1

Question 2 :

Five mangoes and 4 apples are in a box. If two fruits are chosen at random, find the probability that (i) one is a mango and the other is an apple (ii) both are of the same variety.

Solution :

Total number of fruits in a box  =  5 mangoes + 4 apples

=  9

Since we take two fruits from the box, the sample space will be 9C2

9C2    =  (9 ⋅ 8)/(2 ⋅ 1)  =  36

(i) one is a mango and the other is an apple

Let "A" be the event of getting one is a mango and other is an apple.

Thus we select 1 mango from 5 mangoes and 1 apple from 4 apples.

n(A)  =  5C⋅ 4C1

n(A)  =  5 ⋅ 4  =  20

P(A)  =  n(A)/n(S)

=  20/36

P(A)  =  5/9

(ii) both are of the same variety.

Let "B" be the event of getting the probability of both are of the same variety.

n(B)  =  (5C 4C0) + (5C 4C2)

=  10 + 6

n(B)  =  16

P(B)  =  n(B)/n(S)

=  16/36

p(B)  =  4/9

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