? Help with probability, please~
An experiment consists of tossing an unfair coin (59% chance of landing on heads) a specified number of times and recording the outcomes.
(a) What is the probability that the first head will occur on the second trial? (Use 4 decimal places.)
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That's asking for the probability that the coin lands tails first,
and then heads second.
P(heads) = 59% = 0.59
P(tails) = 100% - 59% = 41% = 0.41
P(tails first AND heads second) = P(tails first)×P(heads second) =
(0.41)×(0.59) = 0.2419
[Learn that "AND" means to multiply probabilities, while "OR" means
to add them.
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Does this probability change if we toss the coin three times?
What if we toss the coin four times?
No it doesn't change because we're only interested in what happens
on the first two tosses. It doesn't matter what happens after that.
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What probability distribution model do we use to compute
these probabilities?
A BIcycle has TWO wheels.
When we BIsect something we cut it into TWO parts
The prefix "BI-" means TWO.
There are TWO ways the coin can fall, 1. Heads, 2. Tails.
Answer: BInomial.
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(b) What is the probability that the first head will occur
on the fourth trial?
That's asking for the probability that the coin lands tails first,
tails second, tails third, and heads fourth.
P(heads) = 59% = 0.59
P(tails) = 100% - 59% = 41% = 0.41
P(tails first AND tails second AND tails third AND heads fourth) =
P(tails first)×P(tails second)×P(tails third)×P(heads fourth) =
(0.41)×(0.41)×(0.41)×(0.59) = 0.04066339, round to 0.0407
[Again, be sure to learn that "AND" means to multiply probabilities, while
"OR" means to add them.]
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(b) What is the probability that the first head will occur...
after the fourth trial?
That's asking for the probability that the coin lands tails first,
tails second, tails third, and tails fourth. [It doesn't matter
when the first head occurs, for if the first four tosses are tails,
the first head will occur sometime AFTER the fourth trial.
P(tails first AND tails second AND tails third AND tails fourth) =
P(tails first)×P(tails second)×P(tails third)×P(tails fourth) =
(0.41)×(0.41)×(0.41)×(0.41) = 0.02825761, round to 0.0283.
Edwin