Question

21. A box contains 15 cards numbered 1, 2, 3, ..., 15 which are mixed thoroughly. A card
is drawn from the box at random. Find the probability that the number on the card is :
(1) odd
(ii) prime
(ii) divisible by 3
(iv) divisible by 3 and 2 both
(U) divisible by 3 or 2
(vi) a perfect square number.​

Answer 1

Answer:

numbers in box are=1,2,3 ......15

Step-by-step explanation:

odd numbers from 1 to 15 are 1,3,5,7,9,11,13 ,15

n ( number of outcomes)= 15

n' ( favourable outcomes)=8

probability = possible outcome ÷ by total number of outcomes

probablity = 8÷15

Answer 2

a) P(A)= 8/15

b) P(B)= 1/3

c) P(C)= 1/3

d) P(D)= 2/15

e) P(E)= 2/5

f) P(F)= 1/5

Step-by-step explanation:

a) Let A be the event of getting an odd number

A= {1,3,5,7,9,11,13,15}

n( A) = 8

P(A) = n(A)/n (S)

P (A) = 8/15

b) Let B be the event of getting a prime number

B= {3,5,7,11,13}

n(B) = 5

P (B) = 5/15

P(B) = 1/3

c) Let C be the event of getting a number which is divisible by 3

C = {3,6,9,12,15}

n(C)= 5

P(C)= 1/3

d) Let D be the event of getting a number which is divisible by both 3 and 2

D ={6,12}

n(D)= 2

P(D) = 2/15

e) Let E be the event of getting a number divisible by 3 or 2

Let E1 be the getting of getting a number which is divisible by 3

E1= {3,6,9,12,15}

n(E1)= 5

P(E1)= 5/15

Let E2 be the event of getting a number which is divisible by 2

E2= {2,4,6,8,10,12,14}

n (E2) =7

P(E2)= 7/15

E1 intersection E2 ={6,12}

P(E1 intersection E2) = 2/15

P(E1 union E2)= P(E1)+P(E2)-P(E1 intersection E2)

P(E)=2/5

f) Let F be the event of getting a perfect square number

F={1,4,9}

n(F)=3

P(F)=3/15

P(F)=1/5