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

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Answer 2

Concept

The results of random experiments determine events in probability. Events will be formed in probability by any subset of the sample space.

Probability is a way of calculating how likely something is to happen.

The likelihood or probability that an event will occur is the ratio of favorable outcomes to all outcomes, i.e.

$\[\Probability=\frac{Number\text{ }of\text{ }favorable\text{ }outcomes}{Total\text{ }number\text{ }of\text{ }possible\text{ }outcomes}\]$

Given

There are three 1p coins, five 10p coins, and eight 2p coins in the purse.

Find

We have to find the probabilities of getting a 1p coin, 2p coin, not a 1p coin and a 1p or a 10p coin.

Solution

Total number of coins in the purse is given as-

$3+5+8=16$

This is the total number of possible outcomes.

Now, there are total three 1p coins. This is the number of favorable outcomes.

Therefore, the probability of getting a 1p coin is calculated as-

$=\frac{3}{16}$  ...(1)

Now, there are total eight 2p coins. This is the number of favorable outcomes.

Therefore, the probability of getting a 2p coin is calculated as-

$=\frac{8}{16}\\=\frac{1}{2}$

Now, the probability of not getting a 1p coin is calculated as-

$=1-$probability of getting a 1p coin

Using (1), we get

$=1-\frac{3}{16}\\=\frac{13}{16}$

Now, there are total five 10p coins. This is the number of favorable outcomes.

Therefore, the probability of getting a 1p coin or a 10p coin is calculated as-

$=$probability of getting a 1p coin$+$probability of getting a 10p coin

Using (1), we get

$=\frac{3}{16}+\frac{5}{16}\\=\frac{8}{16}\\=\frac{1}{2}$

Hence, $\frac{3}{16}$, $\frac{1}{2}$, $\frac{13}{16}$, $\frac{1}{2}$, are the required probabilities of getting a 1p coin, 2p coin, not a 1p coin and a 1p or a 10p coin, respectively.

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