Ex 14.1 Q10 - A piggy bank contains hundred 50p coins, fifty ₹1 coins, twenty ₹2 coins and ten ₹5 coins. If it is equally likely that one of the coins will fall out when the bank is turned upside down, what is the probability that the coin (i) will be a 50 p coin ? (ii) will not be a ₹5 coin?
Solution:-Given,
No. of 50p coins = 100
No. of ₹1 coins = 50
No. of ₹2 coins = 20
No. of ₹5 coins = 10
∴ Total coins = 100 + 50 + 20 + 10
= 180
∴ No. of Total outcomes = 180
*Formula to be used:-
P(Event) =
No. of favourable outcomes
/
No. of total outcomes
(i) Will be a 50p coin:-
We have,
No. of 50p coins = 100
(Favourable outcome)
No. of total coins = 180
(Total outcome)
∴ P(getting a 50p coin)
=
No. of 50p coins
/
No. of total coins
=
100
/
180
=
10
/
18
=
5
/
9
∴ P(getting a 50p coin) =
5
/
9
Therefore, the probability of getting a 50p coin is 5/9.
(ii) Will not be a ₹5 coin:-
We have,
No. of ₹5 coins = 10
(Favourable outcome)
No. of total coins = 180
(Total outcome)
∴ P(getting a ₹5 coin)
=
No. of ₹5 coins
/
No. of total coins
=
10
/
180
=
1
/
18
➙ We know that, event of getting a ₹5 coin and event of not getting a ₹5 coin are complimentary event,
∴ P(getting a ₹5 coin) + P(not getting a ₹5 coin) = 1
∴ P(not getting a ₹5 coin)
= 1 - P(getting a ₹5 coin)
= 1 -
1
/
18
=
18 - 1
/
18
=
17
/
18
∴ P(not getting a ₹5 coin) =
17
/
18
Alternatively,
➙ According to question, the coin dropped from the piggy bank should not be of ₹5,
Then, it will be the coin of either 50p, ₹1 or ₹2.
∴ No. of (50p + ₹1 + ₹2) coins
= 100 + 50 + 20
= 170
∴ Favourable outcome = 170
No. of total coins = 180
(Total outcome)
∴ P(not getting a ₹5 coin)
=
No. of coins except ₹5
/
No. of total coins
=
170
/
180
=
17
/
18
∴ P(not getting a ₹5 coin) =
17
/
18
Therefore, the probability of not getting a ₹5 coin is 17/18.
Hence,
The probability of getting a 50p coin and not getting a ₹5 coin is 5/9 and 17/18 respectively.
------------------------------------
Try This..
✒ A bag contains 4 white, 3 black, and 5 red balls. What is the probability that the ball picked is not black?
✒A card is drawn from a deck of 52 cards. What is the probability that it is a king?
✒ A box contains 3 red balls, 5 green balls, and 2 blue balls. Find the probability of getting a green ball.
❌ Common Mistakes
Not calculating total outcomes correctly:▸ Always add all types of coins/items to get the correct total.Mixing up favourable outcomes:▸ Be clear whether the question is asking “what is” or “what is not” (like in part ii).Not reducing fractions:▸ Always simplify the final probability fraction unless it’s already in lowest terms.Confusing coin values with quantity:▸ In probability, we only care about number of coins, not their rupee values!
Queries Solved:-
Class 10 Ex 14.1
Ex 14.1 Q10 Class 10
Class 10 Ex 14.1 Q10
Class 10 Chap 14 Ex 14.1 Q10
Class 10 Probability
If you found it helpful, please leave a comment below sharing your thoughts or questions.
Don’t forget to share it with your classmates to help them learn too.
Good luck, and happy learning!
Together, let’s make math simpler and more enjoyable for everyone!