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  • A student tosses a fair coin and rolls a fair dice. What is the probability that the coin shows heads and the dice shows an even number?Option: 1 <im

A student tosses a fair coin and rolls a fair dice. What is the probability that the coin shows heads and the dice shows an even number?

Option: 1

\frac{1}{2}


Option: 2

\frac{1}{4}


Option: 3

\frac{1}{6}


Option: 4

\frac{1}{8}


Answers (1)

best_answer

To solve this problem, we need to first understand what it means for events to be independent. 

Two events are said to be independent if the outcome of one event does not affect the outcome of the other event. 

In other words, the probability of one event occurring does not change based on whether or not the other event occurs. 

The sample space when a coin is tossed once is:

{E=\left\{ H,T \right\}}

In this case, the probability of getting heads on a fair coin is \frac{1}{2} since there are two equally likely outcomes (heads or tails). 

Now, the sample space when dice is rolled once is:

{F=\left\{ 1,2,3,4,5,6 \right\}}

So, the probability of rolling an even number on a fair dice is  \frac{1}{2}, since there are three even numbers (2, 4, and 6) out of a total of six possible outcomes. 

To find the probability of both events occurring, we simply multiply their individual probabilities. 

Therefore, the probability of getting heads on the coin and rolling an even number on the dice is:

\\{P(\text{heads and even})=P(\text{heads})\times P(\text{even})}\\ \\\Rightarrow {P(\text{heads and even})=\frac{1}{2}\times \frac{1}{2}}\\ \\\Rightarrow {P(\text{heads and even})=\frac{1}{4}}

Therefore, the probability that the coin shows heads and the dice shows as even number is 

\frac{1}{4}

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Nehul

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