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# Probability

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Help meee hard problems

Valeria has three coins, each of which has a probability of 1/2 of coming up heads. On her first turn, she flips all three coins. If all three come up heads, then she stops. Otherwise, for her second turn, she flips any coins that came up tails.  If there are still coins that come up tails, she flips any coins that came up tails, and so on.

(a) What is the probability that Valeria has two heads on her first turn?
(b) What is the probability that Valeria has three heads on her first turn?

(c) What is the probability that Valeria has two heads after her second turn?

(d) What is the probability that Valeria has one head after her second turn?

(e) What is the probability that Valeria has one head after her third turn?

(f) What is the probability that Valeria has three heads after her fourth turn?

Mar 6, 2023

#1
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(a) What is the probability that Valeria has two heads on her first turn?

:-  Assuming that Valeria is flipping two coins on her first turn, the probability of getting two heads is calculated as follows:

The probability of getting a head on a single coin flip is 1/2, since there are two possible outcomes (heads or tails) that are equally likely.

To calculate the probability of getting two heads, we need to multiply the probability of getting a head on the first flip by the probability of getting a head on the second flip, since these are independent events. Thus:

Therefore, the probability that Valeria has two heads on her first turn is 1/4 or 0.25.

Mar 6, 2023
#2
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(b) What is the probability that Valeria has three heads on her first turn?
Ans:- Assuming that Valeria is flipping a fair coin, the probability of getting a heads on any given flip is 0.5 (or 1/2).

The probability of getting three heads in a row on the first three flips is the product of the probabilities of each individual flip coming up heads, since the flips are independent of each other: