Question

In Hannah’s purse there are three 1p coins, five 10p coins and eight 2p coins. She takes a coin at random from her purse. What is the probability of:  

(a) a 1p coin

(b) a 2p coin

(c) not a 1p coin

(d) a 1p coin or 10p coin

​

Answer 1

Answer:

a) 3/16

b) 8/16

c) 13/16

d) 1/2

Step-by-step explanation:

total number of coins = 3+5+8 = 16

P(event) = number of favourable outcomes/total number of outcomes

a) here, 1p coin is the favourable outcome, and since there are 3 1p coins, there are 3 favourable outcome. and there are 16 total outcomes.

therefore, P(1p coin) = 3/16

similarly, in b), P(2p coin) = 8/16

c) not a 1p coin means the coin can be a 2p coin or a 10p coin, which means the number of favourable outcomes = 8+5 = 13

=> P(not 1p coin) = 13/16

d) a 1p coin or 10p coin means that the number of favourable outcomes = 3+5 = 8

=> P(1p or 10p coin) = 8/16 = 1/2

Answer 2

Concept

The probability of getting event A from total events is given as

P = event A/ total events

Also we know that the probability of two independent events are multiplied and two dependent events are added.

Given

There are 3 coins of 1p.

There are 5 coins of 10p.

There are 8 coins of 2p.

Find

We have to calculate the probability of getting a 1p, 2p, not a 1p, a 1p or 10 p coins.

Solution

The total number of coins = 3+5+8

= 16

Therefore, the probability of getting 1p coins = 3/16

Similarly, the probability of getting 2p coins = 8/16

= 1/2

And the probability of getting any coin but not 1 p coins = 1 - (3/16)

= 13/16

Since the total probability is always 1.

The probability of getting 1p or 10p coins = (3/16) + ( 5/16)

= 8/16

=1/2

Hence the probability of getting a 1p, 2p, not a 1p, a 1p or 10 p coins is 3/16, 1/2, 13/16, 1/2 respectively.

#SPJ2