Probability of HAT

NoraP28 · **Joined:** Mon, 30 Jan 2012 05:14:31 UTC **Posts:** 2

3 boxes contain letters

[MATH] [AND] [HISTORY]

a.) From box 1. Draw 3 letters one by one (without replacement) and record them in order. What is the probability that the outcome is HAT?

b.) From box 1. Draw 3 letters one by one ( with replacement) and record them in order. What is the probability that the outcome is HAT?

c.) Draw one letter at random from box 1, another from box 2, and another from box 3. record in order. What is the probability the outcome is HAT?

d.) If a box is chosen at random and then a letter is drawn at random from the box, what is the probability that the outcome will be A?

Soroban · **Posted:** Mon, 30 Jan 2012 14:47:00 UTC

Hello, NoraP28

Quote:

Three boxes contain letters: . $\boxed{\begin{array}{c} 1 \\ M,A,T,H \end{array}} \quad \boxed{\begin{array}{c} 2 \\ A,N,D \end{array}} \quad \boxed{\begin{array}{c} 3 \\ H,I,S,T,O,R,Y \end{array}}$

a) From box 1, draw 3 letters one by one (without replacement) and record them in order.
. . What is the probability that the outcome is HAT?

$$P(\text{HAT}) \:=\:\frac{1}{4}\cdot\frac{1}{3}\cdot\frac{1}{2} \:=\:\frac{1}{24}$

Quote:

b) From box 1, draw 3 letters one by one (with replacement) and record them in order.
. . What is the probability that the outcome is HAT?

$$P(\text{HAT}) \:=\:\frac{1}{4}\cdot\frac{1}{4}\cdot\frac{1}{4} \:=\:\frac{1}{64}$

Quote:

c) Draw one letter at random from box 1, another from box 2, and another from box 3, record in order.
. . What is the probability the outcome is HAT?

$$P(\text{HAT}) \:=\:\frac{1}{4}\cdot\frac{1}{3}\cdot\frac{1}{7} \:=\:\frac{1}{84}$

Quote:

d) If a box is chosen at random and then a letter is drawn at random from the box,
. . what is the probability that the outcome will be A?

$P(\text{Box 1}) \,=\,\frac{1}{3}\,\text{ and }\, P(A) \,=\,\frac{1}{4} \quad\Rightarrow\quad P(\text{Box 1} \wedge A) \:=\:\frac{1}{3}\cdot\frac{1}{4} \:=\:\frac{1}{12}$

$P(\text{Box 2}) \,=\,\frac{1}{3}\:\text{ and }\:P(A) \,=\,\frac{1}{3} \quad\Rightarrow\quad P(\text{Box 2} \wedge A) \:=\:\frac{1}{3}\cdot\frac{1}{3} \:=\:\frac{1}{9}$

$P(\text{Box 3}) \,=\,\frac{1}{3}\,\text{ and }\,P(A) \,=\,0 \quad\Rightarrow\quad P(\text{Box 3} \wedge A) \:=\:\frac{1}{3}\cdot0 \:=\:0$

. . $$\text{Therefore: }\:P(A) \:=\:\frac{1}{12} + \frac{1}{9} + 0 \:=\:\frac{7}{36}$

Shadow · **Posted:** Mon, 30 Jan 2012 14:47:28 UTC

NoraP28 wrote:

3 boxes contain letters

[MATH] [AND] [HISTORY]

a.) From box 1. Draw 3 letters one by one (without replacement) and record them in order. What is the probability that the outcome is HAT?

b.) From box 1. Draw 3 letters one by one ( with replacement) and record them in order. What is the probability that the outcome is HAT?

c.) Draw one letter at random from box 1, another from box 2, and another from box 3. record in order. What is the probability the outcome is HAT?

d.) If a box is chosen at random and then a letter is drawn at random from the box, what is the probability that the outcome will be A?

What have you tried? These are fairly straightforward, for example the first one you need to have H, then A, then T, and there are no repeats, so you just need to multiply probabilities.

NoraP28 · **Joined:** Mon, 30 Jan 2012 05:14:31 UTC **Posts:** 2

It was a matter of not being able to relate the question to examples done in class, I got it already. Thank you though.

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Probability of HAT

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