In an experiment, three people toss a fair coin one at a time until one of them tosses a head. Determine, for each person, the probability that he or she tosses the first head. Verify that the sum of the three probabilities is 1.

Answers

Answer 1

Answer:

Answer:

Players probabilities of winning are 4/7 , 2/7, 1/7 which of course sum to 1.

Step-by-step explanation:

The coin theoretically could give a very large number of tails first so each person's probability is made up of an infinite series.

P(1st person wins) = P(H) + P(TTTH) + P(TTTTTTH) + . . . etc

= 1/2 + (1/2)^4 + (1/2)^7 + (1/2)^10 + . . .

This is a geometric series with first term a = 1/2 and common ratio r = 1/8

Using formula a/(1 - r) this is (1/2)/(7/8) = 4/7

P(2nd person wins) = P(TH) + P(TTTTH) + P(TTTTTTTH)

= (1/2)^2 + (1/2)^5 + (1/2)^8 + . . .

Geometric series with sum (1/4)/(7/8) = 2/7

P(3rd person wins) = P(TTH) + P(TTTTTH) + P(TTTTTTTTH) + . . .

= (1/2)^3 + (1/2)^6 + (1/2)^9 + . . .

Geometric series with sum (1/8)/(7/8) = 1/7

Players probabilities of winning are 4/7 , 2/7, 1/7 which of course sum to 1.

Hope this helped!

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Given: ∠A and ∠B are complementary angles. m∠A=3x+105 ; m∠B=−6x−39 Prove: m∠B=9° Drag and drop reasons into the boxes to correctly complete the proof. Statement Reason ∠A and ∠B are complementary angles. Given
m∠A=3x+105 ; m∠B=−6x−39 Given
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Answers

Answer:

Statement: -3x=90-66

Reason: By subtraction property of equality..

Statement: -3x=24

Reason: By simplification.

Statement: x= $(24)/(-3)$

Reason: By division property of equality.

Statement: $m\angle B= -6(-8)-39$

Reason: By substitution property of equality.

Statement: $m\angle B=9^(\circ)$

Reason: By simplification.

Step-by-step explanation:

Given $\angle A$ and $\angle B$ are complementary angles.

$m\angle A= 3x+105$

$m\angle B=-6x-39$

To prove that $m\angle B=9^(\circ)$

Proof:

1.Statement: $\angle A\; and\; \angle B$ are complementary angles .

Reason: Given .

2.Statement: $m\angle A=3x+105$ ; $m\angle B= -6x-39$

Reason: Given .

3. Statement: $m\angle A+ m\angle B=90^(\circ)$

Reason: By definition of complementary angles.

4.Statement: $3x+105-6x-39=90$

Reason: By substitution property of equality.

5. Statement: $-3x+105-39=90$

Reason: By simplification.

6. Statement: $-3x+66=90$

Reason: By simplification.

7. Statement: $-3x= 90-66$

Reason: By subtraction property of equality .

8.Statement: $-3x=24$

Reason: By simplification.

9.Statement: $x=(24)/(-3)$

Reason : By division property of equality.

10. Statement: x=-8

Reason: By simplification.

11. Statement: $m\angle B= -6(-8)-39$

Reason : By substitution property of equality.

12. Statement: $m\angle B= 48-39$

Reason: By simplification.

13. Statement: $m\angle B=9^(\circ)$

Reason : By simplification.

Hence, $m\angle B= 9^(\circ)$

Hence proved.

Given: $\angle A$ and $\angle B$ are complementary angles.

$m \angle A = 3x+105^\circ$ and $m \angle B = -6x-39^\circ$ .

To prove: $m \angle B = 9^\circ$

Proof:

Statement 1: $\angle A$ and $\angle B$ are complementary angles.

Reason 1: Given

Statement 2: $m \angle A = 3x+105^\circ$ and $m \angle B = -6x-39^\circ$ .

Reason 2: Given

Statement 3: $m \angle A + m \angle B = 90^\circ$

Reason 3: Definition of complementary angles.

Statement 4: $3x+105^\circ -6x -39^\circ = 90^\circ$

Reason 4: Substitution property of equality

Statement 5: $-3x+105^\circ-39^\circ = 90^\circ$

Reason 5: Simplification

Statement 6: $-3x+66^\circ = 90^\circ$

Reason 6: Simplification

Statement 7: $-3x = 24^\circ$

Reason 7: Simplification

Statement 8: $x = -8$

Reason 8: Multiplication property of equality

Statement 9: $m \angle B = -6(-8) - 39^\circ$

Reason 9: Substituting the value of 'x'

Statement 10: $m \angle B = 48-39 = 9^\circ$

Reason 10: Simplification

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Answers

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