Farah rolls a fair dice and flips a fair coin.
What is the probability of obtaining a 5 and a head?
Give your answer in its simplest form.
Answers
Answer:
Short answer: 1/12 (one chance out of 12).
Longer answer
Let’s call the event of of getting a 5 on a single roll of a single fair die “event A”. The probability of A is 1/6. Let’s call that probability P(A) .
P(A)=16
B is the event of getting Heads on a single flip of a fair coin. And its probability is one half.
P(B)=12
When two events are independent then the probability of both of them happening is simply the product of the probability of each. In this problem A and B are independent so the so the probability of both happening, P(A&B) is given by
P(A&B)=P(A)P(B)=112
that is we just multiply P(A) by P(B) .
Non-independence
I emphasized that the events need to be “independent” to be able to simply multiply. Suppose we have event C which which is getting a 4 on the same roll of the die that we use for event A. P(C) is also 1/6. But because this is the very same roll of the die for our event A, the probability of getting both a 4 and a 5 on a single roll of a fair die is not 1/36 (what we would get from multiplying P(A) and P(C) ). Instead in this case, the probably of P(A&C) should be zero.
Of course events can depend on each other in other ways. Consider the event D of “not getting tails” on the same coin flip in event B. Here the chances of “getting heads and not getting tails on a single flip of a fair coin” remains 1/2. which is the same either of P(B) and P(D) . So when judging these things we have to know how the events depend on each other (if they do).
But when, as in your question, the events are independent, you just multiply to probabilities of each to get the probability of the combination of them.
A note about homework questions
If you are going to post homework questions, please make an effort to learn from the answers given. Also be aware that people answering your question may choose to answer with more precision and detail than is useful for the person asking the question. For example, much of this specific question depends on the independence of two events. Someone answering the question might try to explain why independence has the properties that it does based on definitions coming from measure theory. (I didn’t go that far.)
But I probably talked more about independence than was useful to someone asking the simple question you asked. This is because practical probability and statistics gets more interesting when events are not entirely independent. Often, in practice, people are trying to figure out the nature of the interdependence between events.
Note also that mathematicians (and those inclined to answer mathematics questions on Quora will much prefer giving answers like “1/12” instead of “0.08333…” even though your teacher may expect the latter form. (Though I don’t know why any math teacher would prefer that.)
So it is best to try to give some notion in the question details of why you are asking. Are you placing a bet? Is it a homework question (and for what level)? Or is it a question that I didn’t answer in enough detail?
Step-by-step explanation:
Hope you like it!☺️
Answer:
1/12
Step-by-step explanation:
Dice has 6 outcomes in total (1,2,3,4,5,6)
Coin has 2 outcomes in total (Head or Tails)
probability = (Favourable outcome)/ total outcome
probability of getting a 5 = 1/6
probability of getting a head = 1/2
Final probability = 1/6*1/2 = 1/12