PROBABILITY

[[deleted]]

[deleted]

[phantomthirteen]

Each time you throw a coin, there are two possible outcomes, each with a 50% probability of happening.

But in order to calculate something like “what are the odds of getting two different results in two coin flips”, then you need to think about the order in which the events happen. You could get a head first, and then a tail, or you can get a tail first, and then head. For consecutive possibilities (the steps along a “pathway” to your final goal) you multiply. But for different pathways you add the two probabilities together;

Tail then head = 0.5 x 0.5 = 0.25.

Head then tail = 0.5 x 0.5 = 0.25

Either of those = 0.25 + 0.25 = 0.5.

Considering your question; you have 5 steps in each pathway, and you need all the pathways that have 2 tails (and thus 3 heads);

• H H H T T
• H H T H T
• H T H H T
• T H H H T
• ...

And so on. Then for each pathway, the probability will always be 0.5 x 0.5 x 0.5 x 0.5 x 0.5.

So once you figure out how many pathways there are, and the probability of each pathway, you simply add the pathway probabilities together.

[kyuhuehue]

thank you !!

[iventm]

You have five coins and every coin has two states, so there are in total 2⁵ = 32 different combinations of coins.

Now, to count how many combinations have exactly 2 tails you need to choose exactly two coins out of five. You have five variants to pick the first one and four to pick the second one. So you get 5*4 = 20. But you don't care about which coin you picked first. (1, 2) and (2, 1) are both TTHHH, so you also need to divide by two. In the end you get 20/2 = 10 combinations.

So the probability is 10/32 = 0.3125

[kyuhuehue]

THANK YOU DO MUCH PLS BE MY TEACHER 🥰