Ten cards numbered 1 to 10 are placed in a box, mixed up thoroughly and then one card is drawn randomly. If it is known that the number on the card drawn is more than 3, what is the probability that it is an even number ?
Answers
Total number of cards in the box n(S) = {1,2,3,4,5,6,7,8,9,10) = 10.
(i) Let A be the event of drawing a card which is an even number.
= > n(A) = {2,4,6,8,10}
= 5.
Required probability P(A) = n(A)/n(S) = 5/10.
(ii) Let B be the event of drawing a number that is more than 3.
= > n(B) = {4,5,6,7,8,9,10}
= 7.
Required probability p(B) = n(B)/n(S) = 7/10.
Now,
(A ∩ B) = {4,6,8,10}
= 4/10.
We know that P(A/B) = P(A ∩ B)/P(B)
= (4/10) * (10/7)
= (4/7).
Hope it helps!
Answer:
Step-by-step explanation:
Total number of cards in the box n(S) = {1,2,3,4,5,6,7,8,9,10) = 10.
(i) Let A be the event of drawing a card which is an even number.
= > n(A) = {2,4,6,8,10}
= 5.
Required probability P(A) = n(A)/n(S) = 5/10.
(ii) Let B be the event of drawing a number that is more than 3.
= > n(B) = {4,5,6,7,8,9,10}
= 7.
Required probability p(B) = n(B)/n(S) = 7/10.
Now,
(A ∩ B) = {4,6,8,10}
= 4/10.
We know that P(A/B) = P(A ∩ B)/P(B)
= (4/10) * (10/7)
= (4/7).